Abstract: We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems using the language of commutant algebras, the algebra of all operators that commute with each local term that appears in the Hamiltonian or each local gate of the circuit. We provide a precise definition of Hilbert space fragmentation in this formalism as the case where the dimension of the commutant algebra grows exponentially with the system size. Fragmentation can, hence, be distinguished from systems with conventional symmetries such as U(1) or SU(2), where the dimension of the commutant algebra grows polynomially with the system size. Furthermore, the commutant algebra language also helps distinguish between “classical” and “quantum” Hilbert space fragmentation, where the former refers to fragmentation in the product state basis. We explicitly construct the commutant algebra in several systems exhibiting classical fragmentation, including the t−J_z model and the spin-1 dipole-conserving model, and we illustrate the connection to previously studied “statistically localized integrals of motion.” We also revisit the Temperley-Lieb spin chains, including the spin-1 biquadratic chain widely studied in the literature, and show that they exhibit quantum Hilbert space fragmentation. Finally, we study the contribution of the full commutant algebra to the Mazur bounds in various cases. In fragmented systems, we use expressions for the commutant to analytically obtain new or improved Mazur bounds for autocorrelation functions of local operators that agree with previous numerical results. In addition, we are able to rigorously show the localization of the on-site spin operator in the spin-1 dipole-conserving model.

Publication: Physical Review X Vol.: 12 No.: 1 ISSN: 2160-3308

ID: CaltechAUTHORS:20220113-182211896

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Abstract: We study the antiferromagnetic XYZ spin chain with quenched bond randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation using the spectrum-bifurcation renormalization group, and assuming marginal many-body localization, proposed that critical indices vary continuously. In this work, we solve the low-energy physics using an unbiased numerically exact tensor network method named the “rigorous renormalization group.” We find a line of fixed points consistent with infinite-randomness phenomenology, with indeed continuously varying critical exponents for average spin correlations. A self-consistent Hartree–Fock-type treatment of the z couplings as interactions added to the free-fermion random XY model captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We solve the problem of the locally correlated XY spin chain with an arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on an associated classical random walk problem. This is also an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. We argue that this line of fixed points also controls an extended region of the critical interacting XYZ spin chain.

Publication: Physical Review B Vol.: 104 No.: 21 ISSN: 2469-9950

ID: CaltechAUTHORS:20210831-203949345

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Abstract: We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a Z₃ ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with Z₃ × Z₃ global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of SU(3)-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typical of systems realizing deconfined critical points. Nevertheless, we find evidence for a direct transition from the VBS phase to a Z₃ ferromagnet. Finite-entanglement scaling data are consistent with a second-order or weakly first-order transition. We find in our parameter space an integrable lattice model apparently describing the phase transition, with a very long, finite, correlation length of 190878 lattice spacings. Based on exact results for this model, we propose that the transition is extremely weakly first order and is part of a family of deconfined quantum critical points described by walking of renormalization group flows.

Publication: Physical Review B Vol.: 103 No.: 15 ISSN: 2469-9950

ID: CaltechAUTHORS:20201109-081814617

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Abstract: The η-pairing states are a set of exactly known eigenstates of the Hubbard model on hypercubic lattices, first discovered by Yang [C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989)]. These states are not many-body scar states in the Hubbard model because they occupy unique symmetry sectors defined by the so-called η-pairing SU(2) symmetry. We study an extended Hubbard model with bond-charge interactions, popularized by Hirsch [J. E. Hirsch, Physica C 158, 326 (1989)], where the η-pairing states survive without the η-pairing symmetry and become true scar states. We also discuss similarities between the η-pairing states and exact scar towers in the spin-1 XY model found by Schecter and Iadecola [M. Schecter and T. Iadecola, Phys. Rev. Lett. 123, 147201 (2019)], and systematically arrive at all nearest-neighbor terms that preserve such scar towers in one dimension. We also generalize these terms to arbitrary bipartite lattices. Our study of the spin-1 XY model also leads us to several scarred models, including a spin-1/2 J₁−J₂ model with Dzyaloshinskii-Moriya interaction, in realistic quantum magnet settings in one and two dimensions.

Publication: Physical Review B Vol.: 102 No.: 7 ISSN: 2469-9950

ID: CaltechAUTHORS:20200609-072308647

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Abstract: Quantum many-body scar states are exceptional finite energy density eigenstates in an otherwise thermalizing system that do not satisfy the eigenstate thermalization hypothesis. We investigate the fate of exact many-body scar states under perturbations. At small system sizes, deformed scar states described by perturbation theory survive. However, we argue for their eventual thermalization in the thermodynamic limit from the finite-size scaling of the off-diagonal matrix elements. Nevertheless, we show numerically and analytically that the nonthermal properties of the scars survive for a parametrically long time in quench experiments. We present a rigorous argument that lower bounds the thermalization time for any scar state as t∗∼O(λ^(−1/(1+d))), where d is the spatial dimension of the system and λ is the perturbation strength.

Publication: Physical Review Research Vol.: 2 No.: 3 ISSN: 2643-1564

ID: CaltechAUTHORS:20200709-135402210

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Abstract: Quantum many-body scar states are many-body states with finite energy density in non-integrable models that do not obey the eigenstate thermalization hypothesis. Recent works have revealed “towers” of scar states that are exactly known and are equally spaced in energy, specifically in the AKLT and spin-1 XY models, and a spin-1/2 model that conserves the number of domain walls. We provide a common framework to understand and prove known exact towers of scars in these systems, by evaluating the commutator of the Hamiltonian and a ladder operator. In particular, we provide a simple proof of the scar towers in the integer-spin 1D AKLT models by studying two-site spin projectors. Through this picture we deduce a family of Hamiltonians that share the scar tower with the AKLT model, and also find common parent Hamiltonians for the AKLT and XY model scars. We also introduce new towers of exact states, organized in a “pyramid” structure, in the spin-1/2 model through the successive application of a nonlocal ladder operator.

Publication: Physical Review B Vol.: 101 No.: 19 ISSN: 2469-9950

ID: CaltechAUTHORS:20200518-131230068

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Abstract: We study a model of Rydberg atoms in a nearest-neighbor Rydberg blockaded regime, introduced by Lesanovsky [Phys. Rev. Lett. 108, 105301 (2012)]. This many-body model (which has one parameter z) has an exactly known gapped liquid ground state, and two exactly known low-lying excitations. We discover two exact low-lying eigenstates. We also discuss behavior of the model at small parameter z and its proximity to an integrable model. Lastly, we discuss connections between the Lesanovsky model at intermediate z and the so-called PXP model. The PXP model describes a recent experiment that observed unusual revivals from a charge-density-wave initial state, which are attributed to a set of many-body “scar states” which do not obey the eigenstate thermalization hypothesis. We discuss the possibility of approximate scar states in the Lesanovsky model and present two approximations for them.

Publication: Physical Review B Vol.: 101 No.: 9 ISSN: 2469-9950

ID: CaltechAUTHORS:20191223-160336506

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Abstract: Quantum many-body scar states are many-body states with finite energy density in non-integrable models that do not obey the eigenstate thermalization hypothesis. Recent works have revealed "towers" of scar states that are exactly known and are equally spaced in energy, specifically in the AKLT model, the spin-1 XY model, and a spin-1/2 model that conserves number of domain walls. We provide a common framework to understand and prove known exact towers of scars in these systems, by evaluating the commutator of the Hamiltonian and a ladder operator. In particular we provide a simple proof of the scar towers in the integer-spin 1d AKLT models by studying two-site spin projectors. Through this picture we deduce a family of Hamiltonians that share the scar tower with the AKLT model, and also find common parent Hamiltonians for the AKLT and XY model scars. We also introduce new towers of exact states, organized in a "pyramid" structure, in the spin-1/2 model through successive application of a non-local ladder operator.

Publication: arXiv
ID: CaltechAUTHORS:20200303-083407096

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Abstract: A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a charge density wave initial state, and theoretical works identified a set of many-body “scar states” showing nonthermal behavior in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at an infinite temperature that can be represented exactly as matrix product states with a finite bond dimension, for both periodic boundary conditions (two exact E = 0 states) and open boundary conditions (two E = 0 states and one each E = ±√2). This discovery explicitly demonstrates the violation of the strong eigenstate thermalization hypothesis in this model and uncovers exact quantum many-body scar states. These states show signatures of translational symmetry breaking with a period-2 bond-centered pattern, despite being in one dimension at an infinite temperature. We show that the nearby many-body scar states can be well approximated as “quasiparticle excitations” on top of our exact E = 0 scar states and propose a quasiparticle explanation of the strong oscillations observed in experiments.

Publication: Physical Review Letters Vol.: 122 No.: 17 ISSN: 0031-9007

ID: CaltechAUTHORS:20181203-095532141

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Abstract: We perform a numerical study of a spin-1/2 model with ℤ_2 × ℤ_2 symmetry in one dimension which demonstrates an interesting similarity to the physics of two-dimensional deconfined quantum critical points (DQCP). Specifically, we investigate the quantum phase transition between Ising ferromagnetic and valence bond solid (VBS) symmetry-breaking phases. Working directly in the thermodynamic limit using uniform matrix product states, we find evidence for a direct continuous phase transition that lies outside of the Landau-Ginzburg-Wilson paradigm. In our model, the continuous transition is found everywhere on the phase boundary. We find that the magnetic and VBS correlations show very close power-law exponents, which is expected from the self-duality of the parton description of this DQCP. Critical exponents vary continuously along the phase boundary in a manner consistent with the predictions of the field theory for this transition. We also find a regime where the phase boundary splits, as suggested by the theory, introducing an intermediate phase of coexisting ferromagnetic and VBS order parameters. Interestingly, we discover a transition involving this coexistence phase which is similar to the DQCP, being also disallowed by the Landau-Ginzburg-Wilson symmetry-breaking theory.

Publication: Physical Review B Vol.: 99 No.: 16 ISSN: 2469-9950

ID: CaltechAUTHORS:20190429-143530475

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Abstract: We study a one-dimensional (1D) system that shows many analogies to proposed two-dimensional (2D) deconfined quantum critical points (DQCP). Our system is a translationally invariant spin-1/2 chain with onsite Z_2×Z_2 symmetry and time-reversal symmetry. It undergoes a direct continuous transition from a ferromagnet (FM), where one of the Z2 symmetries and the time reversal are broken, to a valence bond solid (VBS), where all onsite symmetries are restored while the translation symmetry is broken. The other Z_2 symmetry remains unbroken throughout, but its presence is crucial for both the direct transition (via specific Berry phase effect on topological defects, also related to a Lieb-Schultz-Mattis–type theorem) and the precise characterization of the VBS phase (which has crystalline-symmetry-protected-topological–like property). The transition has a description in terms of either two domain-wall species that “fractionalize” the VBS order parameter or in terms of two partons that “fractionalize” the FM order parameter, with each picture having its own Z_2 gauge theory structure. The two descriptions are dual to each other and, at long wavelengths, take the form of a self-dual gauged Ashkin-Teller model, reminiscent of the self-dual easy-plane noncompact CP^1 model that arises in the description of the 2D easy-plane DQCP. We also find an exact reformulation of the transition that leads to a simple field-theory description that explicitly unifies the FM and VBS order parameters; this reformulation can be interpreted as a new parton approach that does not attempt to fractionalize either of the FM and VBS order parameters but instead encodes them in instanton operators. Aside from providing explicit realizations of many ideas proposed in the context of the 2D DQCP, here in the simpler and fully tractable 1D setting with continuous transition, our study also suggests a possible line of approach to the 2D DQCP.

Publication: Physical Review B Vol.: 99 No.: 7 ISSN: 2469-9950

ID: CaltechAUTHORS:20181105-090225094

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Abstract: We study out-of-time-ordered correlators (OTOCs) in hard-core boson models with short-range and long-range hopping and compare the results to the OTOCs in the Luttinger-liquid model. For density-density correlations, a related expectation value of the squared commutator starts at zero and decays back to zero after the passage of the wavefront in all three models, while the wavefront broadens as t^(1/3) in the short-range model and shows no broadening in the long-range model and the Luttinger-liquid model. For the boson creation operator, the corresponding commutator function shows saturation inside the light cone in all three models, with similar wavefront behavior as in the density-density commutator function, despite the presence of a nonlocal string in terms of Jordan-Wigner fermions. For the long-range model and the Luttinger-liquid model, the commutator function decays as a power law outside the light cone in the long-time regime when following different fixed-velocity rays. In all cases, the OTOCs approach their long-time values in a power-law fashion, with different exponents for different observables and short-range versus long-range cases. Our long-range model appears to capture exponents in the Luttinger-liquid model (which are found to be independent of the Luttinger parameter in the model). This conclusion also comes to bear on the OTOC calculations in conformal field theories, which we propose correspond to long-ranged models.

Publication: Physical Review B Vol.: 98 No.: 13 ISSN: 2469-9950

ID: CaltechAUTHORS:20180821-145330708

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Abstract: We numerically assess model wave functions for the recently proposed particle-hole-symmetric Pfaffian (“PH-Pfaffian”) topological order, a phase consistent with the recently reported thermal Hall conductance [M. Banerjee et al., Nature 559, 205 (2018)] at the ever enigmatic ν = 5/2 quantum Hall plateau. We find that the most natural Moore-Read-inspired trial state for the PH-Pfaffian, when projected into the lowest Landau level, exhibits a remarkable numerical similarity on accessible system sizes with the corresponding (compressible) composite Fermi liquid. Consequently, this PH-Pfaffian trial state performs reasonably well energetically in the half-filled lowest Landau level, but is likely not a good starting point for understanding the ν = 5/2 ground state. Our results suggest that the PH-Pfaffian model wave function either encodes anomalously weak p-wave pairing of composite fermions or fails to represent a gapped, incompressible phase altogether.

Publication: Physical Review B Vol.: 98 No.: 8 ISSN: 2469-9950

ID: CaltechAUTHORS:20180810-093237801

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Abstract: Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOC in chaotic systems in some aspects. Here we study the OTOC for different operators in the exactly-solvable one-dimensional quantum Ising spin chain. The OTOC for spin operators that are local in terms of the Jordan-Wigner fermions has a “shell-like” structure: After the wavefront passes, the OTOC approaches its original value in the long-time limit, showing no signature of scrambling; the approach is described by a t^(−1) power law at long time t. On the other hand, the OTOC for spin operators that are nonlocal in the Jordan-Wigner fermions has a “ball-like” structure, with its value reaching zero in the long-time limit, looking like a signature of scrambling; the approach to zero, however, is described by a slow power law t^(−1/4) for the Ising model at the critical coupling. These long-time power-law behaviors in the lattice model are not captured by conformal field theory calculations. The mixed OTOC with both local and nonlocal operators in the Jordan-Wigner fermions also has a “ball-like” structure, but the limiting values and the decay behavior appear to be nonuniversal. In all cases, we are not able to define a parametrically large window around the wavefront to extract the Lyapunov exponent.

Publication: Physical Review B Vol.: 97 No.: 14 ISSN: 2469-9950

ID: CaltechAUTHORS:20180418-093907947

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Abstract: We numerically construct translationally invariant quasiconserved operators with maximum range M, which best commute with a nonintegrable quantum spin chain Hamiltonian, up to M = 12. In the large coupling limit, we find that the residual norm of the commutator of the quasiconserved operator decays exponentially with its maximum range M at small M, and turns into a slower decay at larger M. This quasiconserved operator can be understood as a dressed total “spin-z” operator, by comparing with the perturbative Schrieffer-Wolff construction developed to high order reaching essentially the same maximum range. We also examine the operator inverse participation ratio of the operator, which suggests its localization in the operator Hilbert space. The operator also shows an almost exponentially decaying profile at short distance, while the long-distance behavior is not clear due to limitations of our numerical calculation. Further dynamical simulation confirms that the prethermalization-equilibrated values are described by a generalized Gibbs ensemble that includes such quasiconserved operator.

Publication: Physical Review B Vol.: 96 No.: 21 ISSN: 2469-9950

ID: CaltechAUTHORS:20171004-144618632

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Abstract: The success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad et al. [Math. Phys. 356, 65 (2017)]. The convergence proof, however, relies on “rigorous renormalization group” (RRG) techniques which differ fundamentally from existing algorithms. We introduce a practical adaptation of the RRG procedure which, while no longer theoretically guaranteed to converge, finds matrix product state ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in realistic situations. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a treelike manner. We evaluate the algorithm numerically, finding similar performance to density matrix renormalization group (DMRG) in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.

Publication: Physical Review B Vol.: 96 No.: 21 ISSN: 2469-9950

ID: CaltechAUTHORS:20170627-090122309

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Abstract: Recent work on a family of boson-fermion mappings has emphasized the interplay of symmetry and duality: Phases related by a particle-vortex duality of bosons (fermions) are related by time-reversal symmetry in their fermionic (bosonic) formulation. We present exact mappings for a number of concrete models that make this property explicit on the operator level. We illustrate the approach with one- and two-dimensional quantum Ising models and then similarly explore the duality web of complex bosons and Dirac fermions in (2+1) dimensions. We generalize the latter to systems with long-range interactions and discover a continuous family of dualities embedding the previously studied cases.

Publication: Physical Review X Vol.: 7 No.: 4 ISSN: 2160-3308

ID: CaltechAUTHORS:20170525-150801314

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Abstract: We provide an explicit lattice model of bosons with two separately conserved boson species [U(1)×U(1) global symmetry] realizing a direct transition between an integer quantum Hall effect of bosons and a trivial phase, where any intermediate phase is avoided by an additional symmetry interchanging the two species. If the latter symmetry is absent, we find intermediate superfluid phases where one or the other boson species condenses. We know the precise location of the transition since at this point our model has an exact nonlocal antiunitary particle-hole-like symmetry that resembles particle-hole symmetry in the lowest Landau level of electrons. We exactly map the direct transition to our earlier study of the self-dual line of the easy-plane NCCP1 model, in the mathematically equivalent reformulation in terms of two (new) particles with π statistics and identical energetics. While the transition in our model is first order, we hope that our mappings and recent renewed interest in such self-dual models will stimulate more searches for models with a continuous transition.

Publication: Physical Review B Vol.: 96 No.: 11 ISSN: 2469-9950

ID: CaltechAUTHORS:20170920-104241961

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Abstract: The eigenstate thermalization hypothesis provides one picture of thermalization in a quantum system by looking at individual eigenstates. However, it is also important to consider how local observables reach equilibrium values dynamically. Quench protocol is one of the settings to study such questions. A recent numerical study [Bañuls, Cirac, and Hastings, Phys. Rev. Lett. 106, 050405 (2007)] of a nonintegrable quantum Ising model with longitudinal field under such a quench setting found different behaviors for different initial quantum states. One particular case called the “weak-thermalization” regime showed apparently persistent oscillations of some observables. Here we provide an explanation of such oscillations. We note that the corresponding initial state has low energy density relative to the ground state of the model. We then use perturbation theory near the ground state and identify the oscillation frequency as essentially a quasiparticle gap. With this quasiparticle picture, we can then address the long-time behavior of the oscillations. Upon making additional approximations which intuitively should only make thermalization weaker, we argue that the oscillations nevertheless decay in the long-time limit. As part of our arguments, we also consider a quench from a BEC to a hard-core boson model in one dimension. We find that the expectation value of a single-boson creation operator oscillates but decays exponentially in time, while a pair-boson creation operator has oscillations with a t^(−3/2) decay in time. We also study dependence of the decay time on the density of bosons in the low-density regime and use this to estimate decay time for oscillations in the original spin model.

Publication: Physical Review A Vol.: 95 No.: 2 ISSN: 2469-9926

ID: CaltechAUTHORS:20161212-141040765

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Abstract: We introduce a particle-hole-symmetric metallic state of bosons in a magnetic field at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding 2π Berry flux protected by particle-hole and discrete rotation symmetries. We also construct an alternative particle-hole symmetric state—distinct in the presence of inversion symmetry—without Berry flux. As in the Dirac composite Fermi liquid introduced by Son [Phys. Rev. X 5, 031027 (2015)], breaking particle-hole symmetry recovers the familiar Chern-Simons theory. We discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as signatures in experiments and simulations.

Publication: Physical Review Letters Vol.: 117 No.: 13 ISSN: 0031-9007

ID: CaltechAUTHORS:20160518-123950203

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Abstract: We demonstrate that a nonzero concentration nv of static, randomly placed vacancies in graphene leads to a density w of zero-energy quasiparticle states at the band center ε=0 within a tight-binding description with nearest-neighbor hopping t on the honeycomb lattice. We show that wremains generically nonzero in the compensated case (exactly equal number of vacancies on the two sublattices) even in the presence of hopping disorder and depends sensitively on nv and correlations between vacancy positions. For low, but not-too-low, |ε|/t in this compensated case, we show that the density of states ρ(ε) exhibits a strong divergence of the form ρ_(Dyson)(ε)∼|ε|^(-1)/[log(t/|ε|)]^((y+1)), which crosses over to the universal low-energy asymptotic form (modified Gade-Wegner scaling) expected on symmetry grounds ρ_(GW)(ε)∼|ε|^(-1)e^(-b[log(t/|ε|)]2/3) below a crossover scale ε_c≪t. ε_c is found to decrease rapidly with decreasing nv, while y decreases much more slowly.

Publication: Physical Review Letters Vol.: 117 No.: 11 ISSN: 0031-9007

ID: CaltechAUTHORS:20160621-163531479

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Abstract: Quantum phases characterized by surfaces of gapless excitations are known to violate the otherwise ubiquitous boundary law of entanglement entropy in the form of a multiplicative log correction: S∼L^(d−1) log L . Using variational Monte Carlo, we calculate the second Rényi entropy for a model wave function of the ν=1/2 composite Fermi liquid (CFL) state defined on the two-dimensional triangular lattice. By carefully studying the scaling of the total Rényi entropy and, crucially, its contributions from the modulus and sign of the wave function on various finite-size geometries, we argue that the prefactor of the leading L log L term is equivalent to that in the analogous free fermion wave function. In contrast to the recent results of Shao et al. [Phys. Rev. Lett. 114, 206402 (2015)], we thus conclude that the “Widom formula” holds even in this non-Fermi liquid CFL state. More generally, our results further elucidate—and place on a more quantitative footing—the relationship between nontrivial wave function sign structure and S∼L log L entanglement scaling in such highly entangled gapless phases.

Publication: Physical Review B Vol.: 94 No.: 8 ISSN: 2469-9950

ID: CaltechAUTHORS:20160622-104304294

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Abstract: We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in (2+1) dimensions (QED_3) with N=1 fermion flavors. The duality proceeds via an exact, non-local mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED_3 scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and N=2 QED_3.

Publication: Physical Review Letters Vol.: 117 No.: 1 ISSN: 0031-9007

ID: CaltechAUTHORS:20160404-083319765

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Abstract: In a two-dimensional electron gas under a strong magnetic field, correlations generate emergent excitations distinct from electrons. It has been predicted that “composite fermions”—bound states of an electron with two magnetic flux quanta—can experience zero net magnetic field and form a Fermi sea. Using infinite-cylinder density matrix renormalization group numerical simulations, we verify the existence of this exotic Fermi sea, but find that the phase exhibits particle-hole symmetry. This is self-consistent only if composite fermions are massless Dirac particles, similar to the surface of a topological insulator. Exploiting this analogy, we observe the suppression of 2k_F backscattering, a characteristic of Dirac particles. Thus, the phenomenology of Dirac fermions is also relevant to two-dimensional electron gases in the quantum Hall regime.

Publication: Science Vol.: 352 No.: 6282 ISSN: 0036-8075

ID: CaltechAUTHORS:20160404-074621321

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Abstract: We study a statistical mechanics model of two species of bosons with mutual statistics θ=2π/n in (2+1) dimensions. This model realizes a fractionalized topological phase of bosons, which is a fractionalized version of the boson integer quantum Hall effect. The model can be studied with sign-free Monte Carlo simulations. We study the phase transitions between the fractionalized topological phase and a trivial insulator, and between different topological phases. We find that these transitions are continuous, and we measure their critical exponents.

Publication: Physical Review B Vol.: 93 No.: 3 ISSN: 1098-0121

ID: CaltechAUTHORS:20160128-145609595

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Abstract: More than half a century after first being proposed by Sir Nevill Mott, the deceptively simple question of whether the interaction-driven electronic metal-insulator transition may be continuous remains enigmatic. Recent experiments on two-dimensional materials suggest that when the insulator is a quantum spin liquid, lack of magnetic long-range order on the insulating side may cause the transition to be continuous, or only very weakly first order. Motivated by this, we study a half-filled extended Hubbard model on a triangular lattice strip geometry. We argue, through use of large-scale numerical simulations and analytical bosonization, that this model harbors a continuous (Kosterlitz-Thouless-like) quantum phase transition between a metal and a gapless spin liquid characterized by a spinon Fermi surface, i.e., a “spinon metal.” These results may provide a rare insight into the development of Mott criticality in strongly interacting two-dimensional materials and represent one of the first numerical demonstrations of a Mott insulating quantum spin liquid phase in a genuinely electronic microscopic model.

Publication: Physical Review B Vol.: 91 No.: 23 ISSN: 1098-0121

ID: CaltechAUTHORS:20140714-161947260

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Abstract: Topologically ordered phases of matter, in particular so-called symmetry-enriched topological phases, can exhibit quantum number fractionalization in the presence of global symmetry. In Z_2 topologically ordered states in two dimensions, fundamental translations T_x and T_y acting on anyons can either commute or anticommute. This property, crystal momentum fractionalization, can be seen in a periodicity of the excited-state spectrum in the Brillouin zone. We present a numerical method to detect the presence of this form of symmetry enrichment given a projected entangled pair state; we study the minima of the spectrum of correlation lengths of the transfer matrix for a cylinder. As a benchmark, we demonstrate our method using a modified toric code model with perturbation. An enhanced periodicity in momentum clearly reveals the nontrivial anticommutation relation {T_x, T_y}=0 for the corresponding quasiparticles in the system.

Publication: Physical Review B Vol.: 91 No.: 12 ISSN: 1098-0121

ID: CaltechAUTHORS:20150410-083507920

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Abstract: We study a topological phase of interacting bosons in (3 + 1) dimensions that is protected by charge conservation and time-reversal symmetry. We present an explicit lattice model that realizes this phase and that can be studied in sign-free Monte Carlo simulations. The idea behind our model is to bind bosons to topological defects called hedgehogs. We determine the phase diagram of the model and identify a phase where such bound states are proliferated. In this phase, we observe a Witten effect in the bulk whereby an external monopole binds half of the elementary boson charge, which confirms that it is a bosonic topological insulator. We also study the boundary between the topological insulator and a trivial insulator. We find a surface phase diagram that includes exotic superfluids, a topologically ordered phase, and a phase with a Hall effect quantized to one-half of the value possible in a purely two-dimensional system. We also present models that realize symmetry-enriched topologically ordered phases by binding multiple hedgehogs to each boson; these phases show charge fractionalization and intrinsic topological order as well as a fractional Witten effect.

Publication: Physical Review X Vol.: 4 No.: 4 ISSN: 2160-3308

ID: CaltechAUTHORS:20150122-101201662

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Abstract: Motivated by ideas of fractionalization and intrinsic topological order in bosonic models with short-range interactions, we consider similar phenomena in formal lattice gauge theory models. Specifically, we show that a compact quantum electrodynamics (CQED) can have, besides the familiar Coulomb and confined phases, additional unusual confined phases where excitations are quantum lines carrying fractions of the elementary unit of electric field strength. We construct a model that has N-tupled monopole condensation and realizes 1/N fractionalization of the quantum Faraday lines. This phase has another excitation which is a Z_N quantum surface in spatial dimensions five and higher, but can be viewed as a quantum line or a quantum particle in four or three spatial dimensions, respectively. These excitations have statistical interactions with the fractionalized Faraday lines; for example, in three spatial dimensions, the particle excitation picks up a Berry phase of e^i2π/N when going around the fractionalized Faraday line excitation. We demonstrate the existence of this phase by Monte Carlo simulations in (3+1) space-time dimensions.

Publication: Physical Review B Vol.: 90 No.: 21 ISSN: 1098-0121

ID: CaltechAUTHORS:20150115-095007267

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Abstract: We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J_1 and J_2, which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z_2 spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU (2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J_2 , we find a Néel phase and a plaquette valence-bond (PVB) phase with a finite spin gap. From the finite-size scaling of the magnetic order parameter, we estimate that the Néel order vanishes at J_2 /J _1 ≃0.44. For 0.5

ID: CaltechAUTHORS:20140714-131011965

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Abstract: We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-1/2 Heisenberg model on a honeycomb lattice with first (J_1) and second (J_2) neighbor antiferromagnetic interactions, where a Z_2 spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with a width slightly over 15 lattice spacings and a torus up to the size N=2×6×6. With increasing J_2, we find a Néel phase with a vanishing spin gap and a plaquette valence-bond (PVB) phase with a nonzero spin gap. By extrapolating the square of the staggered magnetic moment m_s^2 on finite-size cylinders to the thermodynamic limit, we find the Néel order vanishing at J_2/J_1≃0.22. For 0.25

ID: CaltechAUTHORS:20131125-113942857

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Abstract: In this work we present a set of microscopic U(1) × U(1) models which realize insulating phases with a quantized Hall conductivity σ_(xy). The models are defined in terms of physical degrees of freedom, and can be realized by local Hamiltonians. For one set of these models, we find that σ_(xy) is quantized to be an even integer. The origin of this effect is a condensation of objects made up of bosons of one species bound to a single vortex of the other species. For other models, the Hall conductivity can be quantized as a rational number times two. For these systems, the condensed objects contain bosons of one species bound to multiple vortices of the other species. These systems have excitations carrying fractional charges and non-trivial mutual statistics. We present sign-free reformulations of these models which can be studied in Monte Carlo, and we use such reformulations to numerically detect a gapless boundary between the quantum Hall and trivial insulator states. We also present the broader phase diagrams of the models.

Publication: Annals of Physics Vol.: 334ISSN: 0003-4916

ID: CaltechAUTHORS:20130719-143804802

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Abstract: Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau’s celebrated Fermi liquid theory is of central importance to many outstanding problems in condensed matter physics. Perhaps the most important such pursuit is a full microscopic characterization of the high-T_c cuprate superconductors, where the so-called “strange metal” behavior above T_c near optimal doping is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of such a strange metal quantum phase could possibly shed new light on the interesting low-temperature behavior in the pseudogap regime and on the d-wave superconductor itself. Here, we present a theory for a specific example of a strange metal, which we term the “d-wave metal.” Using variational wave functions, gauge theoretic arguments, and ultimately large-scale DMRG calculations, we establish compelling evidence that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian: the venerable t-J model supplemented with a frustrated electron ring-exchange term, which we study extensively here on the two-leg ladder. These findings constitute one of the first explicit examples of a genuine non-Fermi liquid metal existing as the ground state of a realistic model.

Publication: Nature Vol.: 493 No.: 7430 ISSN: 0028-0836

ID: CaltechAUTHORS:20121102-100712474

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Abstract: We study a U(1)×U(1) system in (2+1) dimensions with long-range interactions and mutual statistics. The model has the same form after the application of operations from the modular group, a property which we call modular invariance. Using the modular invariance of the model, we propose a possible phase diagram. We obtain a sign-free reformulation of the model and study it in Monte Carlo. This study confirms our proposed phase diagram. We use the modular invariance to analytically determine the current-current correlation functions and conductivities in all the phases in the diagram, as well as at special “fixed” points which are unchanged by an operation from the modular group. We numerically determine the order of the phase transitions, and find segments of second-order transitions. For the statistical interaction parameter θ=π, these second-order transitions are evidence of a critical loop phase obtained when both loops are trying to condense simultaneously. We also measure the critical exponents of the second-order transitions.

Publication: Physical Review B Vol.: 86 No.: 24 ISSN: 1098-0121

ID: CaltechAUTHORS:20130122-074509815

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Abstract: We study a U(1) × U(1) system with short-range interactions and mutual θ = 2π/3 statistics in (2+1) dimensions. We are able to reformulate the model to eliminate the sign problem and perform a Monte Carlo study. We find a phase diagram containing a phase with only small loops and two phases with one species of proliferated loop. We also find a phase where both species of loop condense, but without any gapless modes. Lastly, when the energy cost of loops becomes small, we find a phase that is a condensate of bound states, each made up of three particles of one species and a vortex of the other. We define several exact reformulations of the model that allow us to precisely describe each phase in terms of gapped excitations. We propose field-theoretic descriptions of the phases and phase transitions, which are particularly interesting on the “self-dual” line where both species have identical interactions. We also define irreducible responses useful for describing the phases.

Publication: Physical Review B Vol.: 86 No.: 4 ISSN: 1098-0121

ID: CaltechAUTHORS:20120807-095947454

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Abstract: We study a lattice model of interacting loops in three dimensions with a 1/r^2 interaction. Using Monte Carlo methods, we have found that the phase diagram contains a line of second-order phase transitions between a phase where the loops are gapped and a phase where they proliferate. The correlation length exponent and critical conductivity vary continuously along this line. Our model is exactly self-dual at a special point on the critical line, which allows us to calculate the critical conductivity exactly at this point.

Publication: Physical Review B Vol.: 85 No.: 14 ISSN: 1098-0121

ID: CaltechAUTHORS:20120504-094836233

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Abstract: We study a U(1)×U(1) system with two species of loops with mutual π statistics in (2 + 1) dimensions. We are able to reformulate the model in a way that can be studied by Monte Carlo and we determine the phase diagram. In addition to a phase with no loops, we find two phases with only one species of loop proliferated. The model has a self-dual line, a segment of which separates these two phases. Everywhere on the segment, we find the transition to be first-order, signifying that the two loop systems behave as immiscible fluids when they are both trying to condense. Moving further along the self-dual line, we find a phase where both loops proliferate, but they are only of even strength and, therefore, avoid the statistical interactions. We study another model, which does not have this phase, and also find first-order behavior on the self-dual segment.

Publication: Physical Review B Vol.: 85 No.: 4 ISSN: 1098-0121

ID: CaltechAUTHORS:20121102-141056955

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Abstract: We establish compelling evidence for the existence of new quasi-one-dimensional descendants of the d-wave Bose liquid (DBL), an exotic two-dimensional quantum phase of uncondensed itinerant bosons characterized by surfaces of gapless excitations in momentum space [O. I. Motrunich and M. P. A. Fisher Phys. Rev. B 75 235116 (2007)]. In particular, motivated by a strong-coupling analysis of the gauge theory for the DBL, we study a model of hard-core bosons moving on the N-leg square ladder with frustrating four-site ring exchange. Here, we focus on four- and three-leg systems where we have identified two novel phases: a compressible gapless Bose metal on the four-leg ladder and an incompressible gapless Mott insulator on the three-leg ladder. The former is conducting along the ladder and has five gapless modes, one more than the number of legs. This represents a significant step forward in establishing the potential stability of the DBL in two dimensions. The latter, on the other hand, is a fundamentally quasi-one-dimensional phase that is insulating along the ladder but has two gapless modes and incommensurate power-law transverse density-density correlations. While we have already presented results on this latter phase elsewhere [ M. S. Block et al. Phys. Rev. Lett. 106 046402 (2011)], we will expand upon those results in this work. In both cases, we can understand the nature of the phase using slave-particle-inspired variational wave functions consisting of a product of two distinct Slater determinants, the properties of which compare impressively well to a density matrix renormalization group solution of the model Hamiltonian. Stability arguments are made in favor of both quantum phases by accessing the universal low-energy physics with a bosonization analysis of the appropriate quasi-1D gauge theory. We will briefly discuss the potential relevance of these findings to high-temperature superconductors, cold atomic gases, and frustrated quantum magnets.

Publication: Physical Review B Vol.: 84 No.: 24 ISSN: 1098-0121

ID: CaltechAUTHORS:20120123-133929180

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Abstract: We realize a gapless Majorana orbital liquid (MOL) using orbital degrees of freedom and an SU(2)-invariant Majorana spin liquid (MSL) using both spin and orbital degrees of freedom in Kitaev-type models on a two-leg ladder. The models are exactly solvable by Kitaev's parton approach, and we obtain long-wavelength descriptions for both Majorana liquids. The MOL has one gapless mode and power-law correlations in energy at incommensuate wave vectors, while the SU(2) MSL has three gapless modes and power-law correlations in spin, spin-nematic, and local energy observables. We study the stability of such states to perturbations away from the exactly solvable points. We find that both MOL and MSL can be stable against allowed short-range parton interactions. We also argue that both states persist on allowing Z_2 gauge-field fluctuations, in that the number of gapless modes is retained, although with an expanded set of contributions to observables compared to the free parton mean field.

Publication: Physical Review B Vol.: 84 No.: 23 ISSN: 1098-0121

ID: CaltechAUTHORS:20120206-111342766

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Abstract: We extended the Schwinger boson construction to obtain wave functions that are resonating valence bond (RVB) counterparts of the degenerate coplanar classical states on the kagome lattice. We examined all 84 of them on the 36-site cluster and found that they form a narrow energy band. On the 12-site cluster, there are only four such states and their superpositions accurately account for the second through fourth exact diagonalization (ED) states, while the ED ground state is accurately reproduced by allowing a particular two-vison insertion on top of the q=0 RVB state. Thus, we have established the RVB sign structures for the low-energy states on this cluster.

Publication: Physical Review B Vol.: 84 No.: 19 ISSN: 1098-0121

ID: CaltechAUTHORS:20111209-132748123

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Abstract: We construct an exactly solvable spin-orbital model on a decorated square lattice that realizes an SU(2)-invariant Majorana spin liquid with parton Fermi surfaces, of the kind discussed recently by Biswas et al. [Phys. Rev. B. 83 245131 (2011)]. We find power-law spin correlations as well as power-law spin-nematic correlations with the same dominant 1/|r|^3 envelope. The model is solvable also in the presence of Zeeman magnetic field. One fermion species carries S^z = 0 quantum number and its Fermi surface is not altered in the field, while the Fermi surfaces of the other species evolve and can disappear. In particular, we find an interesting half magnetization plateau phase in which spin excitations are gapful while there remain spinless gapless excitations that still produce metal-like thermal properties. In the fully magnetized phase, the model reduces to the one proposed by Baskaran et al. [e-print arXiv:0908.1614 (to be published)] in terms of the orbital degrees of freedom.

Publication: Physical Review B Vol.: 84 No.: 8 ISSN: 1098-0121

ID: CaltechAUTHORS:20110921-141634254

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Abstract: Motivated by the unabating interest in the spin-1/2 Heisenberg antiferromagnetic model on the kagome lattice, we investigate the energetics of projected Schwinger-boson (SB) wave functions in the J_(1)-J_(2) model with antiferromagnetic J_(2) coupling. Our variational Monte Carlo results show that Sachdev’s Q_(1)=Q_(2) SB ansatz has a lower energy than the Dirac spin liquid for J_(2) ≳ 0.08J_(1) and the q=0 Jastrow-type magnetically ordered state. This work demonstrates that the projected SB wave functions can be tested on the same footing as their fermionic counterparts.

Publication: Physical Review B Vol.: 84 No.: 2 ISSN: 1098-0121

ID: CaltechAUTHORS:20110801-133149483

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Abstract: Slave particle approaches are widely used in studies of exotic quantum phases. A complete description beyond mean field also contains dynamical gauge fields, while a simplified procedure considers Gutzwiller-projected trial states. We apply this in the context of bosonic models with ring exchanges realizing so-called exciton Bose liquid (EBL) phase and compare a Gutzwiller wave function against an accurate EBL wave function. We solve the parton-gauge theory and show that dynamical fluctuations of the spatial gauge fields are necessary for obtaining qualitatively accurate EBL description. On the contrary, just the Gutzwiller projection leads to a state with subtle differences in the long-wavelength properties, thus suggesting that Gutzwiller wave functions may generally fail to capture long-wavelength physics.

Publication: Physical Review B Vol.: 83 No.: 23 ISSN: 1098-0121

ID: CaltechAUTHORS:20110624-094212541

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Abstract: We investigate a hard-core boson model with ring-only exchanges on a square lattice, where a K_1 term acts on 1×1 plaquettes and a K_2 term acts on 1×2 and 2×1 plaquettes, with a goal of realizing a novel exciton Bose liquid (EBL) phase first proposed by Paramekanti et al. [Phys. Rev. B 66, 054526 (2002)]. We construct Jastrow-type variational wave functions for the EBL, study their formal properties, and then use them as seeds for a projective quantum Monte Carlo study. Using the Green’s function Monte Carlo approach, we obtain an unbiased phase diagram that at half-filling reveals a charge density wave for small K_2, a valence bond solid for intermediate K_2, and possibly for large K_2 the EBL phase. Away from half-filling, the EBL phase is present for intermediate K_2 and remains stable for a range of densities below 1/2 before phase separation occurs at lower densities.

Publication: Physical Review B Vol.: 83 No.: 20 ISSN: 0163-1829

ID: CaltechAUTHORS:20110603-094323218

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Abstract: We study a spin-1/2 system with Heisenberg plus ring exchanges on a four-leg triangular ladder using the density matrix renormalization group and Gutzwiller variational wave functions. Near an isotropic lattice regime, for moderate to large ring exchanges we find a spin Bose-metal phase with a spinon Fermi sea consisting of three partially filled bands. Going away from the triangular towards the square lattice regime, we find a staggered dimer phase with dimers in the transverse direction, while for small ring exchanges the system is in a featureless rung phase. We also discuss parent states and a possible phase diagram in two dimensions.

Publication: Physical Review Letters Vol.: 106 No.: 15 ISSN: 0031-9007

ID: CaltechAUTHORS:20110503-132834831

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Abstract: We study bond energy correlation functions in an exactly solvable quantum spin model of Kitaev type on the kagome lattice with stable Fermi surface of partons proposed recently by Chua et al. [arXiv:1010.1035v1]. Even though any spin correlations are of ultrashort range, we find that the bond energy correlations have power-law behavior with a 1/|r|^3 envelope and oscillations at incommensurate wave vectors. We determine the corresponding singular surfaces in momentum space, which provide a gauge-invariant characterization of this gapless spin liquid.

Publication: Physical Review B Vol.: 83 No.: 15 ISSN: 1098-0121

ID: CaltechAUTHORS:20110422-132229622

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Abstract: We present evidence for an exotic gapless insulating phase of hard-core bosons on multileg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at ν=1/3 filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other N-leg systems and to N-layer two-dimensional structures.

Publication: Physical Review Letters Vol.: 106 No.: 4 ISSN: 0031-9007

ID: CaltechAUTHORS:20110301-084205536

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Abstract: We consider electrons on a two-leg triangular ladder at half filling and in an orbital magnetic field. In a two-band regime in the absence of the field, the electronic system remains conducting for weak interactions since there is no four-fermion umklapp term. We find that in the presence of the orbital field there is a four-fermion umklapp and it is always relevant for repulsive interactions. Thus in this special ladder, the combination of the orbital magnetic field and interactions provides a mechanism to drive metal-insulator transition already at weak coupling. We discuss properties of the possible resulting phases C0S2 and various C0S1 and C0S0.

Publication: Physical Review B Vol.: 82 No.: 19 ISSN: 0163-1829

ID: CaltechAUTHORS:20101215-090601625

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Abstract: We present a quantum Monte Carlo study of a hard-core boson model with ring-only exchanges on a square lattice, where a K_1 term acts on 1×1 plaquettes and a K_2 term acts on 1×2 and 2×1 plaquettes. At half-filling, the phase diagram reveals charge density wave for small K_2, valence bond solid for intermediate K_2, and possibly for large K_2 the novel exciton Bose liquid (EBL) phase first proposed by Paramekanti et al [Phys. Rev. B 66, 054526 (2002)]. Away from half-filling, the EBL phase is present already for intermediate K_2 and remains stable for a range of densities below 1/2 before phase separation sets in at lower densities.

Publication: Physical Review Letters Vol.: 105 No.: 18 ISSN: 0031-9007

ID: CaltechAUTHORS:20101110-105823754

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Abstract: We consider Zeeman field effects on a spin Bose-metal (SBM) phase on a two-leg triangular ladder. This phase was found in a spin-1/2 model with ring exchanges [D. N. Sheng, O. I. Motrunich, and M. P. A. Fisher, Phys. Rev. B 79, 205112 (2009)] and was also proposed to appear in an interacting electronic model with longer-ranged repulsion [H.-H. Lai and O. I. Motrunich, Phys. Rev. B 81, 045105 (2010)]. Using bosonization of a spinon-gauge theory, we study the stability of the SBM phase and its properties under the field. We also explore phases arising from potential instabilities of the SBM; in all cases, we find a gap to spin-1 excitations while spin-nematic correlations are power law. We discuss two-dimensional analogues of these phases where spinons can pair with their own species.

Publication: Physical Review B Vol.: 82 No.: 12 ISSN: 0163-1829

ID: CaltechAUTHORS:20101011-143452308

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Abstract: We present a variational study of the Heisenberg antiferromagnet on the spatially anisotropic triangular lattice in magnetic field. First we construct a simple yet accurate wave function for the 1/3-magnetization plateau uud phase on the isotropic lattice. Beginning with this state, we obtain natural extensions to nearby commensurate coplanar phases on either side of the plateau. The latter occur also for low lattice anisotropy while the uud state extends to much larger anisotropy. Far away from the 1/3 plateau and for significant anisotropy, incommensurate states have better energetics, and we address competition between coplanar and noncoplanar states in the high-field regime. For very strong anisotropy, our study is dominated by quasi-one-dimensional physics. The variational study is supplemented by exact diagonalization calculations which provide a reference for testing the energetics of our trial wave functions as well as helping to identify candidate phases.

Publication: Physical Review B Vol.: 81 No.: 16 ISSN: 1098-0121

ID: CaltechAUTHORS:20100527-104046961

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Abstract: We consider an electronic model for realizing the spin Bose-metal (SBM) phase on a two-leg triangular strip—a spin liquid phase found by Sheng et al. [Phys. Rev. B 79, 205112 (2009)] in a spin-1/2 model with ring exchanges. The SBM can be viewed as a “C1S2” Mott insulator of electrons where the overall charge transporting mode is gapped out. We start from a two-band “C2S2” metal and consider extended repulsion motivated by recent ab initio derivation of electronic model for κ-ET spin liquid material [K. Nakamura et al., J. Phys. Soc. Jpn. 78, 083710 (2009)]. Using weak coupling renormalization group analysis, we find that the extended interactions allow much wider C2S2 metallic phase than in the Hubbard model with on-site repulsion only. An eight-fermion umklapp term plays a crucial role in producing a Mott insulator but cannot be treated in weak coupling. We use bosonization to extend the analysis to intermediate coupling and study phases obtained out of the C2S2 metal upon increasing overall repulsion strength, finding that the SBM phase is a natural outcome for extended interactions.

Publication: Physical Review B Vol.: 81 No.: 4 ISSN: 1098-0121

ID: CaltechAUTHORS:20100217-110938767

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Abstract: We introduce an interlayer coherent composite Fermi liquid for ν=1/2+1/2 bilayers, in which interlayer Coulomb repulsion drives exciton condensation of composite fermions. As a result, composite fermions propagate coherently between layers—even though electrons do not—and form bonding and antibonding Fermi seas. This phase is compressible with respect to symmetric currents but quantum Hall-like in the counterflow channel. Quantum oscillations of the composite Fermi seas generate a new series of incompressible states at ν=p/[2(p±1)] per layer (p an integer), which is a bilayer analogue of Jain’s sequence.

Publication: Physical Review Letters Vol.: 103 No.: 25 ISSN: 0031-9007

ID: CaltechAUTHORS:20100114-143033701

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Abstract: We study the effects of nonmagnetic impurities in a spin Bose-metal (SBM) phase discovered in a two-leg triangular strip spin-1/2 model with ring exchanges (D. N. Sheng et al., arXiv:0902.4210). This phase is a quasi-one-dimensional (quasi-1D) descendant of a two-dimensional (2D) spin liquid with spinon Fermi sea and the present study aims at interpolating between the 1D and 2D cases. Different types of defects can be treated as local-energy perturbations, which we find are always relevant. As a result, a nonmagnetic impurity generically cuts the system into two decoupled parts. We calculate bond energy and local spin susceptibility near the defect, both of which can be measured in experiments. The spin Bose metal has dominant correlations at characteristic incommensurate wave vectors that are revealed near the defect. Thus, the bond energy shows a static texture oscillating as a function of distance from the defect and decaying as a slow power law. The local spin susceptibility also oscillates and actually increases as a function of distance from the defect, similar to the effect found in the 1D chain [S. Eggert and I. Affleck, Phys. Rev. Lett. 75, 934 (1995)]. We calculate the corresponding power-law exponents for the textures as a function of one Luttinger parameter of the SBM theory.

Publication: Physical Review B Vol.: 79 No.: 23 ISSN: 1098-0121

ID: CaltechAUTHORS:20090827-141808367

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Abstract: Recent experiments on triangular lattice organic Mott insulators have found evidence for a two-dimensional (2D) spin liquid in close proximity to the metal-insulator transition. A Gutzwiller wave function study of the triangular lattice Heisenberg model with a four-spin ring exchange term appropriate in this regime has found that the projected spinon Fermi sea state has a low variational energy. This wave function, together with a slave particle-gauge theory analysis, suggests that this putative spin liquid possesses spin correlations that are singular along surfaces in momentum space, i.e., “Bose surfaces.” Signatures of this state, which we will refer to as a “spin Bose metal” (SBM), are expected to manifest in quasi-one-dimensional (quasi-1D) ladder systems: the discrete transverse momenta cut through the 2D Bose surface leading to a distinct pattern of 1D gapless modes. Here, we search for a quasi-1D descendant of the triangular lattice SBM state by exploring the Heisenberg plus ring model on a two-leg triangular strip (zigzag chain). Using density matrix renormalization group (DMRG) supplemented by variational wave functions and a bosonization analysis, we map out the full phase diagram. In the absence of ring exchange the model is equivalent to the J_1-J_2 Heisenberg chain, and we find the expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange reveals a new gapless phase over a large swath of the phase diagram. Spin and dimer correlations possess singular wave vectors at particular “Bose points” (remnants of the 2D Bose surface) and allow us to identify this phase as the hoped for quasi-1D descendant of the triangular lattice SBM state. We use bosonization to derive a low-energy effective theory for the zigzag spin Bose metal and find three gapless modes and one Luttinger parameter controlling all power law correlations. Potential instabilities out of the zigzag SBM give rise to other interesting phases such as a period-3 valence bond solid or a period-4 chirality order, which we discover in the DMRG. Another interesting instability is into a spin Bose-metal phase with partial ferromagnetism (spin polarization of one spinon band), which we also find numerically using the DMRG.

Publication: Physical Review B Vol.: 79 No.: 20 ISSN: 1098-0121

ID: CaltechAUTHORS:20090825-154329286

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Abstract: We study effects of nonmagnetic impurities in a spin-1/2 frustrated triangular antiferromagnet with the aim of understanding the observed broadening of 13C NMR lines in the organic spin liquid material κ-(ET)2Cu2(CN)3. For high temperatures down to J/3, we calculate local susceptibility near a nonmagnetic impurity and near a grain boundary for the nearest-neighbor Heisenberg model in high-temperature series expansion. We find that the local susceptibility decays to the uniform one in few lattice spacings, and for a low density of impurities we would not be able to explain the line broadening present in the experiments already at elevated temperatures. At low temperatures, we assume a gapless spin liquid with a Fermi surface of spinons. We calculate the local susceptibility in the mean field and also go beyond the mean field by Gutzwiller projection. The zero-temperature local susceptibility decays as a power law and oscillates at 2kF. As in the high-temperature analysis we find that a low density of impurities is not able to explain the observed broadening of the lines. We are thus led to conclude that there is more disorder in the system. We find that a large density of pointlike disorder gives broadening that is consistent with the experiment down to about 5 K, but that below this temperature additional mechanism is likely needed.

Publication: Physical Review B Vol.: 79 No.: 2 ISSN: 1098-0121

ID: CaltechAUTHORS:GREprb09

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Abstract: Developing a theoretical framework to access the quantum phases of itinerant bosons or fermions in two dimensions that exhibit singular structure along surfaces in momentum space but have no quasiparticle description remains a central challenge in the field of strongly correlated physics. In this paper we propose that distinctive signatures of such two-dimensional (2D) strongly correlated phases will be manifest in quasi-one-dimensional “N-leg ladder” systems. Characteristic of each parent 2D quantum liquid would be a precise pattern of one-dimensional (1D) gapless modes on the N-leg ladder. These signatures could be potentially exploited to approach the 2D phases from controlled numerical and analytical studies in quasi-one-dimension. As a first step we explore itinerant-boson models with a frustrating ring-exchange interaction on the two-leg ladder, searching for signatures of the recently proposed two-dimensional d-wave-correlated Bose liquid (DBL) phase. A combination of exact diagonalization, density-matrix renormalization-group, variational Monte Carlo, and bosonization analysis of a quasi-1D gauge theory provide compelling evidence for the existence of an unusual strong-coupling phase of bosons on the two-leg ladder, which can be understood as a descendant of the two-dimensional DBL. We suggest several generalizations to quantum spin and electron Hamiltonians on ladders, which could likewise reveal fingerprints of such 2D non-Fermi-liquid phases.

Publication: Physical Review B Vol.: 78 No.: 5 ISSN: 1098-0121

ID: CaltechAUTHORS:SHEprb08

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Abstract: Motivated by recent experiments on ZnCu3(OH)6Cl2, we study the inhomogeneous Knight shifts (local susceptibilities) of a spin-1/2 kagome antiferromagnet in the presence of nonmagnetic impurities. Using high temperature series expansion, we calculate the local susceptibility and its histogram down to about T=0.4J. At low temperatures, we explore a Dirac spin liquid proposal and calculate the local susceptibility in the mean field and beyond mean field using Gutzwiller projection, finding the overall picture to be consistent with the NMR experiments.

Publication: Physical Review B Vol.: 77 No.: 18 ISSN: 1098-0121

ID: CaltechAUTHORS:GREprb08

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Abstract: We study spin S=1 and S=3/2 Heisenberg antiferromagnets on a cubic lattice focusing on spin-solid ground states. Using Schwinger boson formulation for spins, we start in a U(1) spin-liquid phase proximate to Néel phase and explore possible confining paramagnetic phases as we transition away from the spin liquid by the process of monopole condensation. Electromagnetic duality is used to rewrite the theory in terms of monopoles. For spin 1 we find several candidate phases of which the most natural one is a phase with spins organized into parallel Haldane chains. For spin 3/2 we find that the most natural phase has spins organized into parallel ladders. As a by-product, we also write a Landau theory of the ordering in two special classical frustrated XY models on the cubic lattice, one of which is the fully frustrated XY model. In a particular limit our approach maps to a dimer model with 2S dimers coming out of every site, and we find the same spin-solid phases in this regime as well.

Publication: Physical Review B Vol.: 76 No.: 17 ISSN: 1098-0121

ID: CaltechAUTHORS:GREprb07

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Abstract: We develop a description of a quantum liquid phase of interacting bosons confined in two dimensions that possesses relative d-wave two-body correlations. We refer to this stable quantum phase as a d-wave Bose liquid (DBL). The DBL has no broken symmetries, supports gapless boson excitations that reside on “Bose surfaces” in momentum space, and exhibits power-law correlation functions characterized by a manifold of continuously variable exponents. While the DBL can be constructed for bosons moving in the two-dimensional continuum, the state only respects the point group symmetries of the square lattice. On the square lattice, the DBL respects all symmetries and does not require a particular lattice filling. However, lattice effects do allow for the possibility of a second distinct phase, a quasilocal variant we refer to as a d-wave local Bose liquid (DLBL). Remarkably, the DLBL has short-range boson correlations and hence no Bose surfaces, despite sharing gapless excitations and other critical signatures with the DBL. Moreover, both phases are metals with a resistance that vanishes as a power of the temperature. We establish these results by constructing a class of many-particle wave functions for the DBL, which are time reversal invariant analogs of Laughlin's quantum Hall wave function for bosons in a half-filled Landau level. A gauge theory formulation leads to a simple mean field theory, and a suitable N-flavor generalization enables incorporation of gauge field fluctuations to deduce the properties of the DBL/DLBL in a controlled and systematic fashion. Various equal-time correlation functions thereby obtained are in qualitative accord with the properties inferred from the variational wave functions. We also identify a promising microscopic Hamiltonian that might manifest the DBL or DLBL, and perform a variational energetics study comparing other competing phases, including the superfluid. We suggest how the d-wave Bose liquid wave function can be suitably generalized to describe an itinerant non-Fermi-liquid phase of electrons on the square lattice with a no-double-occupancy constraint, a d-wave metal phase.

Publication: Physical Review B Vol.: 75 No.: 23 ISSN: 1098-0121

ID: CaltechAUTHORS:MOTprb07

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Abstract: There is growing evidence from both experiment and numerical studies that low half-odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near-neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength. Moreover, there appears to be a plethora of low-energy excitations, predominantly singlets but also spin carrying, which suggests that the putative underlying quantum spin liquid is a gapless “critical spin liquid” rather than a gapped spin liquid with topological order. Here, we develop an effective field theory approach for the spin-(1/2) Heisenberg model with easy-plane anisotropy on the kagome lattice. By employing a vortex duality transformation, followed by a fermionization and flux smearing, we obtain access to a gapless yet stable critical spin liquid phase, which is described by (2+1)-dimensional quantum electrodynamics (QED3) with an emergent SU(8) flavor symmetry. The specific heat, thermal conductivity, and dynamical structure factor are extracted from the effective field theory, and contrasted with other theoretical approaches to the kagome antiferromagnet.

Publication: Physical Review B Vol.: 75 No.: 18 ISSN: 1098-0121

ID: CaltechAUTHORS:RYUprb07

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Abstract: We explore spin-(1/2) triangular antiferromagnets with both easy-plane and lattice exchange anisotropies by employing a dual vortex mapping followed by a fermionization of the vortices. Over a broad range of exchange anisotropy, this approach leads naturally to a "critical" spin liquid—the algebraic vortex liquid—which appears to be distinct from other known spin liquids. We present a detailed characterization of this state, which is described in terms of noncompact QED3 with an emergent SU(4) symmetry. Descendant phases of the algebraic vortex liquid are also explored, which include the Kalmeyer-Laughlin spin liquid, a variety of magnetically ordered states such as the well-known coplanar spiral state, and supersolids. In the range of exchange anisotropy where the "square lattice" Néel ground state arises, we demonstrate that anomalous "roton" minima in the excitation spectrum recently reported in series expansions can be accounted for within our approach.

Publication: Physical Review B Vol.: 73 No.: 17 ISSN: 1098-0121

ID: CaltechAUTHORS:ALIprb06

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Abstract: We consider orbital magnetic field effects in a spin liquid phase of a half-filled triangular lattice Hubbard system close to the Mott transition, continuing an earlier exploration of a state with spinon Fermi surface. Starting from the Hubbard model and focusing on the insulator side, we derive an effective spin Hamiltonian up to four-spin exchanges in the presence of magnetic field, and find that the magnetic field couples linearly to spin chirality on the triangles. The latter corresponds to a flux of an internal gauge field in a gauge theory description of the spin liquid, and therefore a static internal flux is induced. A quantitative estimate of the effect is obtained using a spinon mean-field analysis, where we find that this orbital field experienced by the spinons is comparable to or even larger than the applied field. We further argue that because the stiffness of the emergent internal gauge field is very small, such a spinon-gauge system is strongly susceptible at low temperatures to an instability of the homogeneous state due to strong Landau level quantization for spinons. This instability is reminiscent of the so-called strong magnetic interaction regime in metals with the usual electromagnetic field, but we estimate that the corresponding temperature–magnetic-field range is significantly broader in the spinon-gauge system.

Publication: Physical Review B Vol.: 73 No.: 15 ISSN: 1098-0121

ID: CaltechAUTHORS:MOTprb06

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Abstract: Motivated by inelastic neutron scattering data on Cs2CuCl4, we explore spin-1/2 triangular lattice antiferromagnets with both spatial and easy-plane exchange anisotropies, the latter due to an observed Dzyaloshinskii-Moriya interaction. Exploiting a duality mapping followed by a fermionization of the dual vortex degrees of freedom, we find a novel critical spin-liquid phase described in terms of Dirac fermions with an emergent global SU(4) symmetry minimally coupled to a noncompact U(1) gauge field. This "algebraic vortex liquid" supports gapless spin excitations and universal power-law correlations in the dynamical spin structure factor which are consistent with those observed in Cs2CuCl4. We suggest future neutron scattering experiments that should help distinguish between the algebraic vortex liquid and other spin liquids and quantum critical points previously proposed in the context of Cs2CuCl4.

Publication: Physical Review Letters Vol.: 95 No.: 24 ISSN: 0031-9007

ID: CaltechAUTHORS:ALIprl05

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Abstract: We reexamine two-dimensional frustrated quantum magnetism with the aim of exploring new critical points and critical phases. We study easy-plane triangular antiferromagnets using a dual vortex approach, fermionizing the vortices with a Chern-Simons field. Herein we develop this technique for integer-spin systems which generically exhibit a simple paramagnetic phase as well as magnetically ordered phases with coplanar and collinear spin order. Within the fermionized-vortex approach, we derive a low-energy effective theory containing Dirac fermions with two flavors minimally coupled to a U(1) and a Chern-Simons gauge field. At criticality we argue that the Chern-Simons gauge field can be subsumed into the U(1) gauge field, and up to irrelevant interactions one arrives at quantum electrodynamics in 2+1 dimensions (QED3). Moreover, we conjecture that critical QED3 with full SU(2) flavor symmetry describes the O(4) multicritical point of the spin model where the paramagnet and two magnetically ordered phases merge. The remarkable implication is that QED3 with flavor SU(2) symmetry is dual to ordinary critical Φ^4 field theory with O(4) symmetry. This leads to a number of unexpected, verifiable predictions for QED3. A connection of our fermionized-vortex approach with the dipole interpretation of the nu=1/2 fractional quantum Hall state is also demonstrated. The approach introduced in this paper will be applied to spin-1/2 systems in a forthcoming publication.

Publication: Physical Review B Vol.: 72 No.: 6 ISSN: 1098-0121

ID: CaltechAUTHORS:ALIprb05

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Abstract: We study triangular lattice spin-1/2 system with antiferromagnetic Heisenberg and ring exchanges using variational approach focusing on possible realization of spin-liquid states. Trial spin liquid wave functions are obtained by Gutzwiller projection of fermionic mean-field states and their energetics is compared against magnetically ordered trial states. We find that in a range of the ring exchange coupling upon destroying the antiferromagnetic order, the best such spin liquid state is essentially a Gutzwiller-projected Fermi sea state. We propose this spin liquid with a spinon Fermi surface as a candidate for the nonmagnetic insulating phase observed in the organic compound kappa-(ET)2Cu2(CN)3, and describe some experimental consequences of this proposal.

Publication: Physical Review B Vol.: 72 No.: 4 ISSN: 1098-0121

ID: CaltechAUTHORS:MOTprb05b

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Abstract: Several simple models of strongly correlated bosons on three-dimensional lattices have been shown to possess exotic fractionalized Mott insulating phases with a gapless "photon" excitation. In this paper we show how to view the physics of this "Coulomb" state in terms of the excitations of proximate superfluid. We argue for the presence of ordered vortex cores with a broken discrete symmetry in the nearby superfluid phase and that proliferating these degenerate but distinct vortices with equal amplitudes produces the Coulomb phase. This provides a simple physical description of the origin of the exotic excitations of the Coulomb state. The physical picture is formalized by means of a dual description of three-dimensional bosonic systems in terms of fluctuating quantum mechanical vortex loops. Such a dual formulation is extensively developed. It is shown how the Coulomb phase (as well as various other familiar phases) of three-dimensional bosonic systems may be described in this vortex loop theory. For bosons at half-filling and the closely related system of spin-1/2 quantum magnets on a cubic lattice, fractionalized phases as well as bond- or "box"-ordered states are possible. The latter are analyzed by an extension of techniques previously developed in two spatial dimensions. The relation between these "confining" phases with broken translational symmetry and the fractionalized Coulomb phase is exposed.

Publication: Physical Review B Vol.: 71 No.: 12 ISSN: 1098-0121

ID: CaltechAUTHORS:MOTprb05a

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Abstract: We study the effect of hedgehog suppression in the O(3) sigma model in D = 2 + 1. We show via Monte Carlo simulations that the sigma model can be disordered while effectively forbidding these point topological defects. The resulting paramagnetic state has gauge charged matter with half-integer spin (spinons) and also an emergent gauge field (photons), whose existence is explicitly demonstrated. Hence, this is an explicit realization of fractionalization in a model with global SU(2) symmetry. The zero-temperature ordering transition from this phase is found to be continuous but distinct from the regular Heisenberg ordering transition. We propose that these phases and this phase transition are captured by the noncompact CP1 model, which contains a pair of bosonic fields coupled to a noncompact U(1) gauge field. Direct simulation of the transition in this model yields critical exponents that support this claim. The easy-plane limit of this model also displays a continuous zero temperature ordering transition, which has the remarkable property of being self-dual. The presence of emergent gauge charge and hence Coulomb interactions is evidenced by the presence of a finite temperature Kosterlitz-Thouless transition associated with the thermal ionization of the gauge charged spinons. Generalization to higher dimensions and the effects of nonzero hedgehog fugacity are discussed.

Publication: Physical Review B Vol.: 70 No.: 7 ISSN: 1098-0121

ID: CaltechAUTHORS:MOTprb04c

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Abstract: We study the extended Hubbard model on a triangular lattice near doping x = (1/3), which may be relevant for the recently discovered superconductor NaxCoO2·yH2O. By generalizing this model to N fermionic species, we formulate a meanfield description in the limit of large N. In meanfield, we find two possible phases: a renormalized Fermi liquid and a sqrt(3)×sqrt(3) charge density wave state. The transition between the two phases is driven by increasing the nearest-neighbor repulsion and is found to be first order for doping x = (1/3), but occurs close to the point of the local instability of the uniform liquid. We also study fluctuations about the uniform meanfield state in a systematic 1/N expansion, focusing on the residual interaction of quasiparticles and possible superconducting instabilities due to this interaction. Upon moving towards the charge density wave instability, the increasing charge fluctuations favor a particular f-wave triplet state. (This state was recently discussed by Tanaka et al., cond-mat/0311266.) We also report a direct Gutzwiller wave function study of the spin-(1/2) model.

Publication: Physical Review B Vol.: 70 No.: 2 ISSN: 0163-1829

ID: CaltechAUTHORS:MOTprb04b

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Abstract: Charge frustration due to further neighbor Coulomb repulsion can have dramatic effects on the electronic properties of NaxCoO2 in the full doping range. It can significantly reduce the effective mobility of the charge carriers, leading to a low degeneracy temperature epsilonF<~T. Such strongly renormalized Fermi liquid has rather unusual properties—from the point of view of the ordinary metals with epsilonFT—but similar to the properties that are actually observed in the NaxCoO2 system. For example, we show that the anomalous thermopower and Hall effect observed in Na0.7CoO2 may be interpreted along these lines. If the repulsion is strong, it can also lead to charge order; nevertheless, away from the commensurate dopings, the configurational constraints allow some mobility for the charge carriers, i.e., there remains some "metallic" component. Finally, the particularly strong bandwidth suppression around the commensurate x = 1/3 can help resurrect the resonating valence bond superconductivity, which would otherwise not be expected near this high doping. These suggestions are demonstrated specifically for a tJ-like model with an additional nearest-neighbor repulsion.

Publication: Physical Review B Vol.: 69 No.: 21 ISSN: 0163-1829

ID: CaltechAUTHORS:MOTprb04a

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Abstract: A bosonic model with unfrustrated hopping and short-range repulsive interactions is constructed that realizes a Z3 fractionalized insulator phase in two dimensions and in zero magnetic field. Such a phase is characterized as having gapped charged excitations that carry fractional electrical charge 1/3 and also gapped Z3 vortices above the topologically ordered ground state.

Publication: Physical Review B Vol.: 67 No.: 11 ISSN: 0163-1829

ID: CaltechAUTHORS:MOTprb03

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Abstract: We show that simple Bose Hubbard models with unfrustrated hopping and short range two-body repulsive interactions can support stable fractionalized phases in two and higher dimensions, and in zero magnetic field. The simplicity of the constructed models advances the possibility of a controlled experimental realization and novel applications of such unconventional states.

Publication: Physical Review Letters Vol.: 89 No.: 27 ISSN: 0031-9007

ID: CaltechAUTHORS:MOTprl02b

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Abstract: We present the design, manufacturing methods, and characterization of 20 microwave feed horns currently in use on the Microwave Anisotropy Probe (MAP) satellite. The nature of the cosmic microwave background (CMB) anisotropy requires a detailed understanding of the properties of every optical component of a microwave telescope. In particular, the properties of the feeds must be known so that the forward gain and sidelobe response of the telescope can be modeled and so that potential systematic effects may be computed. MAP requires low emissivity, azimuthally symmetric, low-sidelobe feeds in five microwave bands (K, K_a, Q, V, and W) that fit within a constrained geometry. The beam pattern of each feed is modeled and compared with measurements; the agreement is generally excellent to the -60 dB level (80° from the beam peak). This agreement verifies the beam-predicting software and the manufacturing process. The feeds also affect the properties and modeling of the microwave receivers. To this end, we show that the reflection from the feeds is less than -25 dB over most of each band and that their emissivity is acceptable. The feeds meet their multiple requirements.

Publication: Astrophysical Journal Supplement Series Vol.: 143 No.: 2 ISSN: 0067-0049

ID: CaltechAUTHORS:20111101-143159282

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Abstract: We construct explicit examples of microscopic models that stabilize a variety of fractionalized phases of strongly correlated systems in a spatial dimension larger than one, and in a zero external magnetic field. These include models of charge fractionalization in boson-only systems, and various kinds of spin-charge separation in electronic systems. We determine the excitation spectrum, and show the consistency with that expected from field theoretic descriptions of fractionalization. Our results are further substantiated by direct numerical calculation of the phase diagram of one of the models.

Publication: Physical Review B Vol.: 66 No.: 20 ISSN: 0163-1829

ID: CaltechAUTHORS:SENprb02

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Abstract: We revisit two-dimensional particle-hole symmetric sublattice localization problem, focusing on the origin of the observed singularities in the density of states ρ(E) at the band center E=0. The most general system of this kind [R. Gade, Nucl. Phys. B 398, 499 (1993)] exhibits critical behavior and has ρ(E) that diverges stronger than any integrable power law, while the special random vector potential model of Ludwig et al. [Phys. Rev. B 50, 7526 (1994)] has instead a power-law density of states with a continuously varying dynamical exponent. We show that the latter model undergoes a dynamical transition with increasing disorder—this transition is a counterpart of the static transition known to occur in this system; in the strong-disorder regime, we identify the low-energy states of this model with the local extrema of the defining two-dimensional Gaussian random surface. Furthermore, combining this “surface fluctuation” mechanism with a renormalization group treatment of a related vortex glass problem leads us to argue that the asymptotic low-E behavior of the density of states in the general case is ρ(E)∼E^-1e-c|ln E|^2/3, different from earlier prediction of Gade. We also study the localized phases of such particle-hole symmetric systems and identify a Griffiths “string” mechanism that generates singular power-law contributions to the low-energy density of states in this case.

Publication: Physical Review B Vol.: 65 No.: 6 ISSN: 0163-1829

ID: CaltechAUTHORS:MOTprb02a

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Abstract: We introduce a strong-disorder renormalization group (RG) approach suitable for investigating the quasiparticle excitations of disordered superconductors in which the quasiparticle spin is not conserved. We analyze one-dimensional models with this RG and with elementary transfer matrix methods. We find that such models with broken spin rotation invariance generically lie in one of two topologically distinct localized phases. Close enough to the critical point separating the two phases, the system has a power-law divergent low-energy density of states (with a nonuniversal continuously varying power law) in either phase, due to quantum Griffiths singularities. This critical point belongs to the same infinite-disorder universality class as the one-dimensional particle-hole symmetric Anderson localization problem, while the Griffiths phases in the vicinity of the transition are controlled by lines of strong (but not infinite) disorder fixed points terminating in the critical point.

Publication: Physical Review B Vol.: 63 No.: 22 ISSN: 0163-1829

ID: CaltechAUTHORS:MOTprb01b

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Abstract: We present results on the low-frequency dynamical and transport properties of random quantum systems whose low temperature (T), low-energy behavior is controlled by strong-disorder fixed points. We obtain the momentum- and frequency-dependent dynamic structure factor in the random singlet (RS) phases of both spin-1/2 and spin-1 random antiferromagnetic chains, as well as in the random dimer and Ising antiferromagnetic phases of spin-1/2 random antiferromagnetic chains. We show that the RS phases are unusual “spin metals” with divergent low-frequency spin conductivity at T=0, and we also follow the conductivity through “metal-insulator” transitions tuned by the strength of dimerization or Ising anisotropy in the spin-1/2 case, and by the strength of disorder in the spin-1 case. We work out the average spin and energy autocorrelations in the one-dimensional random transverse-field Ising model in the vicinity of its quantum critical point. All of the above calculations are valid in the frequency-dominated regime ω≳T, and rely on previously available renormalization group schemes that describe these systems in terms of the properties of certain strong-disorder fixed-point theories. In addition, we obtain some information about the behavior of the dynamic structure factor and dynamical conductivity in the opposite “hydrodynamic” regime ω

ID: CaltechAUTHORS:MOTprb01a

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Abstract: We present the first results on the low-frequency dynamical and transport properties of random antiferromagnetic spin chains at low temperature (T). We obtain the momentum and frequency dependent dynamic structure factor in the random singlet (RS) phases of both spin-1/2 and spin-1 chains, as well as in the random dimer phase of spin-1/2 chains. We also show that the RS phases are unusual “spin-metals” with divergent low-frequency conductivity at T = 0, and follow the spin conductivity through “metal-insulator” transitions tuned by the strength of dimerization or Ising anisotropy in the spin-1/2 case and by the strength of disorder in the spin-1 case.

Publication: Physical Review Letters Vol.: 84 No.: 15 ISSN: 0031-9007

ID: CaltechAUTHORS:DAMprl00

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Abstract: We examine the ground state of the random quantum Ising model in a transverse field using a generalization of the Ma-Dasgupta-Hu renormalization group (RG) scheme. For spatial dimensionality d=2, we find that at strong randomness the RG flow for the quantum critical point is towards an infinite-randomness fixed point, as in one dimension. This is consistent with the results of a recent quantum Monte Carlo study by Pich et al. [Phys. Rev. Lett. 81, 5916 (1998)], including estimates of the critical exponents from our RG that agree well with those from the quantum Monte Carlo. The same qualitative behavior appears to occur for three dimensions; we have not yet been able to determine whether or not it persists to arbitrarily high d. Some consequences of the infinite-randomness fixed point for the quantum critical scaling behavior are discussed. Because frustration is irrelevant in the infinite-randomness limit, the same fixed point should govern both ferromagnetic and spin-glass quantum critical points. This RG maps the random quantum Ising model with strong disorder onto a novel type of percolation/aggregation process.

Publication: Physical Review B Vol.: 61 No.: 2 ISSN: 0163-1829

ID: CaltechAUTHORS:MOTprb00

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Abstract: In the scalar Aharonov-Bohm effect, a charged particle (electron) interacts with the scalar electrostatic potential U in the field-free (i.e., force-free) region inside an electrostatic cylinder (Faraday cage). Using a perfect single-crystal neutron interferometer we have performed a “dual” scalar Aharonov-Bohm experiment by subjecting polarized thermal neutrons to a pulsed magnetic field. The pulsed magnetic field was spatially uniform, precluding any force on the neutrons. Aligning the direction of the pulsed magnetic field to the neutron magnetic moment also rules out any classical torque acting to change the neutron polarization. The observed phase shift is purely quantum mechanical in origin. A detailed description of the experiment, performed at the University of Missouri Research Reactor, and its interpretation is given in this paper.

Publication: Physical Review A Vol.: 60 No.: 6 ISSN: 1050-2947

ID: CaltechAUTHORS:ALLpra99

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Abstract: We have carried out a neutron interferometry experiment using longitudinally polarized neutrons to observe the scalar Aharonov-Bohm effect. The neutrons inside the interferometer are polarized parallel to an applied pulsed magnetic field B(t). The pulsed B field is spatially uniform so it exerts no force on the neutrons. Its direction also precludes the presence of any classical torque to change the neutron polarization.

Publication: Physical Review Letters Vol.: 80 No.: 15 ISSN: 0031-9007

ID: CaltechAUTHORS:LEEprl98

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