Article records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 18:00:20 +0000Boson localization and the superfluid-insulator transition
https://resolver.caltech.edu/CaltechAUTHORS:FISprb89
Authors: Fisher, Matthew P. A.; Weichman, Peter B.; Grinstein, G.; Fisher, Daniel S.
Year: 1989
DOI: 10.1103/PhysRevB.40.546
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ''ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ''Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential. The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary λ transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents ν and η which satisfy the bounds ν≥2/d and η≤2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension dc which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on 4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the λ transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.https://authors.library.caltech.edu/records/9x3c1-bb653Charge accumulation on a Luttinger liquid
https://resolver.caltech.edu/CaltechAUTHORS:20200225-123359485
Authors: Alicea, Jason; Bena, Cristina; Balents, Leon; Fisher, Matthew P. A.
Year: 2004
DOI: 10.1103/physrevb.69.155332
The average charge Q on a quantum wire, modeled as a single-channel Luttinger liquid (LL), connected to metallic leads and coupled to a gate is studied theoretically. We find that the behavior of the charge as the gate voltage V_G varies depends strongly on experimentally adjustable parameters (length, contact transmission, temperature, …). When the intrinsic backscattering at the contacts is weak (i.e., the conductance is close to 2e²/h at high temperature), we predict that this behavior should be described by a universal function. For short such wires, the charge increases roughly linearly with V_G, with small oscillations due to quantum interference between electrons scattered at the contacts. For longer wires at low temperature, Coulomb blockade behavior sets in, and the charge increases in steps. In both limits ∂Q/∂V_G, which should characterize the linear-response conductance, exhibits periodic peaks in V_G. We show that due to Coulomb interactions the period in the former limit is twice that of the latter, and describe the evolution of the peaks through this crossover. The study can be generalized to multichannel LL's, and may explain qualitatively the recent observation by Liang et al. [Phys. Rev. Lett. 88, 126801 (2002)] of a four-electron periodicity for electron addition in single-walled carbon nanotubes.https://authors.library.caltech.edu/records/4vfph-v9g61Transition to zero resistance in a two-dimensional electron gas driven with microwaves
https://resolver.caltech.edu/CaltechAUTHORS:20200225-123359397
Authors: Alicea, Jason; Balents, Leon; Fisher, Matthew P. A.; Paramekanti, Arun; Radzihovsky, Leo
Year: 2005
DOI: 10.1103/physrevb.71.235322
High-mobility two-dimensional electron systems in a perpendicular magnetic field exhibit zero-resistance states (ZRSs) when driven with microwave radiation. We study the nonequilibrium phase transition into the ZRS using phenomenological equations of motion to describe the electron current and density fluctuations in the presence of a magnetic field. We focus on two models to describe the transition into a time-independent steady state. In model I the equations of motion are invariant under a global uniform change in the density. This model is argued to describe physics on small length scales where the density does not vary appreciably from its mean. The ordered state that arises in this case spontaneously breaks rotational invariance in the plane and consists of a uniform current and a transverse Hall field. We discuss some properties of this state, such as stability to fluctuations and the appearance of a Goldstone mode associated with the continuous symmetry breaking. Using dynamical renormalization group techniques, we find that with short-range interactions this model can admit a continuous transition described by mean-field theory, whereas with long-range interactions the transition is driven first order. In model II, we relax the invariance under global density shifts as appropriate for describing the system on longer length scales, and in this case we predict a first-order transition with either short- or long-range interactions. We discuss implications for experiments, including a possible way to detect the Goldstone mode in the ZRS, scaling relations expected to hold in the case of an apparent continuous transition into the ZRS, and a possible signature of a first-order transition in larger samples. Our framework for describing the phase transition into the ZRS also highlights the connection of this problem to the well-studied phenomenon of "bird flocking."https://authors.library.caltech.edu/records/zwtqf-hz834Criticality in quantum triangular antiferromagnets via fermionized vortices
https://resolver.caltech.edu/CaltechAUTHORS:ALIprb05
Authors: Alicea, Jason; Motrunich, Olexei I.; Hermele, Michael; Fisher, Matthew P. A.
Year: 2005
DOI: 10.1103/PhysRevB.72.064407
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.https://authors.library.caltech.edu/records/46cr9-s3274Vortices and Quasiparticles near the Superconductor-Insulator Transition in Thin Films
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Authors: Galitski, Victor M.; Refael, G.; Fisher, Matthew P. A.; Senthil, T.
Year: 2005
DOI: 10.1103/PhysRevLett.95.077002
We study the low temperature behavior of an amorphous superconducting film driven normal by a perpendicular magnetic-field (B). For this purpose we introduce a new two-fluid formulation consisting of fermionized field-induced vortices and electrically neutralized Bogoliubov quasiparticles (spinons) interacting via a long-ranged statistical interaction. This approach allows us to access a novel non-Fermi-liquid phase, which naturally interpolates between the low B superconductor and the high B normal metal. We discuss the properties of the resulting "vortex metal" phase.https://authors.library.caltech.edu/records/wvf22-gg979Algebraic Vortex Liquid in Spin-1/2 Triangular Antiferromagnets: Scenario for Cs2CuCl4
https://resolver.caltech.edu/CaltechAUTHORS:ALIprl05
Authors: Alicea, Jason; Motrunich, Olexei I.; Fisher, Matthew P. A.
Year: 2005
DOI: 10.1103/PhysRevLett.95.247203
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.https://authors.library.caltech.edu/records/k4te2-v7j91Universal point contact resistance between thin-film superconductors
https://resolver.caltech.edu/CaltechAUTHORS:HERprb06
Authors: Hermele, Michael; Refael, Gil; Fisher, Matthew P. A.; Goldbart, Paul M.
Year: 2006
DOI: 10.1103/PhysRevB.73.134504
A system comprising two superconducting thin films connected by a point contact is considered. The contact resistance is calculated as a function of temperature and film geometry, and is found to vanish rapidly with temperature, according to a universal, nearly activated form, becoming strictly zero only at zero temperature. At the lowest temperatures, the activation barrier is set primarily by the superfluid stiffness in the films, and displays only a weak (i.e., logarithmic) temperature dependence. The Josephson effect is thus destroyed, albeit only weakly, as a consequence of the power-law-correlated superconducting fluctuations present in the films below the Berezinskii-Kosterlitz-Thouless transition temperature. The behavior of the resistance is discussed, both in various limiting regimes and as it crosses over between these regimes. Details are presented of a minimal model of the films and the contact, and of the calculation of the resistance. A formulation in terms of quantum phase-slip events is employed, which is natural and effective in the limit of a good contact. However, it is also shown to be effective even when the contact is poor and is, indeed, indispensable, as the system always behaves as if it were in the good-contact limit at low enough temperature. A simple mechanical analogy is introduced to provide some heuristic understanding of the nearly activated temperature dependence of the resistance. Prospects for experimental tests of the predicted behavior are discussed, and numerical estimates relevant to anticipated experimental settings are provided.https://authors.library.caltech.edu/records/qkerg-zct30Theory of the algebraic vortex liquid in an anisotropic spin-(1/2) triangular antiferromagnet
https://resolver.caltech.edu/CaltechAUTHORS:ALIprb06
Authors: Alicea, Jason; Motrunich, Olexei I.; Fisher, Matthew P. A.
Year: 2006
DOI: 10.1103/PhysRevB.73.174430
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.https://authors.library.caltech.edu/records/h774g-pw174Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
https://resolver.caltech.edu/CaltechAUTHORS:20200225-123359309
Authors: Alicea, Jason; Fisher, Matthew P. A.
Year: 2006
DOI: 10.1103/physrevb.74.075422
Starting from the graphene lattice tight-binding Hamiltonian with an on-site U and long-range Coulomb repulsion, we derive an interacting continuum Dirac theory governing the low-energy behavior of graphene in an applied magnetic field. Initially, we consider a clean graphene system within this effective theory and explore integer quantum Hall ferromagnetism stabilized by exchange from the long-range Coulomb repulsion. We study in detail the ground state and excitations at ν=0 and ν=±1, taking into account small symmetry-breaking terms that arise from the lattice-scale interactions, and also explore the ground states selected at ν=±3, ±4, and ±5. We argue that the ferromagnetic regime may not yet be realized in current experimental samples, which at the above filling factors perhaps remain paramagnetic due to strong disorder. In an attempt to access the latter regime where the role of exchange is strongly suppressed by disorder, we apply Hartree theory to study the effects of interactions. Here, we find that Zeeman splitting together with symmetry-breaking interactions can in principle produce integer quantum Hall states in a paramagnetic system at ν=0, ±1, and ±4, but not at ν=±3 or ±5, consistent with recent experiments in high magnetic fields. We make predictions for the activation energies in these quantum Hall states which will be useful for determining their true origin.https://authors.library.caltech.edu/records/d28df-awc04Critical spin liquid at ⅓ magnetization in a spin-½ triangular antiferromagnet
https://resolver.caltech.edu/CaltechAUTHORS:20200225-123359220
Authors: Alicea, Jason; Fisher, Matthew P. A.
Year: 2007
DOI: 10.1103/physrevb.75.144411
Although magnetically ordered at low temperatures, the spin-½ triangular antiferromagnet Cs₂CuCl₄ exhibits remarkable spin dynamics that strongly suggest proximity to a spin-liquid phase. Here we ask whether a proximate spin liquid may also occur in an applied magnetic field, leaving a similar imprint on the dynamical spin correlations of this material. Specifically, we explore a spatially anisotropic Heisenberg spin-½ triangular antiferromagnet at ⅓ magnetization from a dual vortex perspective, and indeed find a "critical" spin-liquid phase described by quantum electrodynamics in (2+1)-dimensions with an emergent SU(6) symmetry. A number of nontrivial predictions follow for the dynamical spin structure factor in this "algebraic vortex liquid" phase, which can be tested via inelastic neutron scattering. We also discuss how well-studied "up-up-down" magnetization plateaus can be captured within our approach, and further predict the existence of a stable gapless solid phase in a weakly ordered up-up-down state. Finally, we predict several anomalous "roton" minima in the excitation spectrum in the regime of lattice anisotropy where the canted Néel state appears.https://authors.library.caltech.edu/records/h79wd-t9186Algebraic vortex liquid theory of a quantum antiferromagnet on the kagome lattice
https://resolver.caltech.edu/CaltechAUTHORS:RYUprb07
Authors: Ryu, S.; Motrunich, O. I.; Alicea, J.; Fisher, Matthew P. A.
Year: 2007
DOI: 10.1103/PhysRevB.75.184406
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.https://authors.library.caltech.edu/records/rrk0z-yc692d-wave correlated critical Bose liquids in two dimensions
https://resolver.caltech.edu/CaltechAUTHORS:MOTprb07
Authors: Motrunich, Olexei I.; Fisher, Matthew P. A.
Year: 2007
DOI: 10.1103/PhysRevB.75.235116
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.https://authors.library.caltech.edu/records/zrgfs-8jy08Interplay between lattice-scale physics and the quantum Hall effect in graphene
https://resolver.caltech.edu/CaltechAUTHORS:20200225-123400068
Authors: Alicea, Jason; Fisher, Matthew P. A.
Year: 2007
DOI: 10.1016/j.ssc.2007.06.035
Graphene's honeycomb lattice structure underlies much of the remarkable physics inherent in this material, most strikingly through the formation of two "flavors" of Dirac cones for each spin. In the quantum Hall regime, the resulting flavor degree of freedom leads to an interesting problem when a Landau level is partially occupied. Namely, while Zeeman splitting clearly favors polarizing spins along the field, precisely how the states for each flavor are occupied can become quite delicate. Here we focus on clean graphene sheets in the regime of quantum Hall ferromagnetism, and discuss how subtler lattice-scale physics, arising either from interactions or disorder, resolves this ambiguity to measurable consequence. Interestingly, such lattice-scale physics favors microscopic symmetry-breaking order coexisting with the usual liquid-like quantum Hall physics emerging on long length scales. The current experimental situation is briefly reviewed in light of our discussion.https://authors.library.caltech.edu/records/kn9j1-jjp25Universal Periods in Quantum Hall Droplets
https://resolver.caltech.edu/CaltechAUTHORS:FIEprl07
Authors: Fiete, Gregory A.; Refael, Gil; Fisher, Matthew P. A.
Year: 2007
DOI: 10.1103/PhysRevLett.99.166805
Using the hierarchy picture of the fractional quantum Hall effect, we study the ground-state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum Hall interferometers. Our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. The model may also provide an experimentally feasible method of detecting elusive neutral modes and otherwise obtaining information about the microscopic edge structure in fractional quantum Hall states.https://authors.library.caltech.edu/records/s6hv2-4yj60Strong-coupling phases of frustrated bosons on a two-leg ladder with ring exchange
https://resolver.caltech.edu/CaltechAUTHORS:SHEprb08
Authors: Sheng, D. N.; Motrunich, Olexei I.; Trebst, Simon; Gull, Emanuel; Fisher, Matthew P. A.
Year: 2008
DOI: 10.1103/PhysRevB.78.054520
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.https://authors.library.caltech.edu/records/dq4mz-j5b39Spin Bose-metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip
https://resolver.caltech.edu/CaltechAUTHORS:20090825-154329286
Authors: Sheng, D. N.; Motrunich, Olexei I.; Fisher, Matthew P. A.
Year: 2009
DOI: 10.1103/PhysRevB.79.205112
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.https://authors.library.caltech.edu/records/denn3-ph063Interlayer Coherent Composite Fermi Liquid Phase in Quantum Hall Bilayers
https://resolver.caltech.edu/CaltechAUTHORS:20100114-143033701
Authors: Alicea, Jason; Motrunich, Olexei I.; Refael, G.; Fisher, Matthew P. A.
Year: 2009
DOI: 10.1103/PhysRevLett.103.256403
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.https://authors.library.caltech.edu/records/6sbfx-hf809Exotic Gapless Mott Insulators of Bosons on Multileg Ladders
https://resolver.caltech.edu/CaltechAUTHORS:20110301-084205536
Authors: Block, Matthew S.; Mishmash, Ryan V.; Kaul, Ribhu K.; Sheng, D. N.; Motrunich, Olexei I.; Fisher, Matthew P. A.
Year: 2011
DOI: 10.1103/PhysRevLett.106.046402
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.https://authors.library.caltech.edu/records/2bexr-3yd20Spin Bose-Metal and Valence Bond Solid Phases in a Spin-1/2 Model with Ring Exchanges on a Four-Leg Triangular Ladder
https://resolver.caltech.edu/CaltechAUTHORS:20110503-132834831
Authors: Block, Matthew S.; Sheng, D. N.; Motrunich, Olexei I.; Fisher, Matthew P. A.
Year: 2011
DOI: 10.1103/PhysRevLett.106.157202
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.https://authors.library.caltech.edu/records/xsn7d-wjk42Non-Abelian statistics and topological quantum information processing in 1D wire networks
https://resolver.caltech.edu/CaltechAUTHORS:20110524-084153167
Authors: Alicea, Jason; Oreg, Yuval; Refael, Gil; von Oppen, Felix; Fisher, Matthew P. A.
Year: 2011
The synthesis of a quantum computer remains an ongoing challenge in modern physics. Whereas decoherence stymies most approaches, topological quantum computation schemes evade decoherence at the hardware level by storing quantum information non-locally. Here we establish that a key operation—braiding of non-Abelian anyons—can be implemented using one-dimensional semiconducting wires. Such wires can be driven into a topological phase supporting long-sought particles known as Majorana fermions that can encode topological qubits. We show that in wire networks, Majorana fermions can be meaningfully braided by simply adjusting gate voltages, and that they exhibit non-Abelian statistics like vortices in a p+ip superconductor. We propose experimental set-ups that enable probing of the Majorana fusion rules and the efficient exchange of arbitrary numbers of Majorana fermions. This work should open a new direction in topological quantum computation that benefits from physical transparency and experimental feasibility.https://authors.library.caltech.edu/records/cbske-gh304Interaction effects in topological superconducting wires supporting Majorana fermions
https://resolver.caltech.edu/CaltechAUTHORS:20200225-123359964
Authors: Stoudenmire, E. M.; Alicea, Jason; Starykh, Oleg A.; Fisher, Matthew P. A.
Year: 2011
DOI: 10.1103/physrevb.84.014503
Among the broad spectrum of systems predicted to exhibit topological superconductivity and Majorana fermions, one-dimensional wires with strong spin-orbit coupling provide one of the most promising experimental candidates. Here we investigate the fate of the topological superconducting phase in such wires when repulsive interactions are present. Using a combination of density matrix renormalization group, bosonization, and Hartree–Fock techniques, we demonstrate that while interactions degrade the bulk gap—consistent with recent results of Gangadharaiah et al.—they also greatly expand the parameter range over which the topological phase arises. In particular, we show that with interactions this phase can be accessed over a broader chemical potential window, thereby leading to greater immunity against disorder-induced chemical potential fluctuations in the wire. We also suggest that in certain wires strong interactions may allow Majorana fermions to be generated without requiring a magnetic field.https://authors.library.caltech.edu/records/xx7gb-zx620Bose metals and insulators on multileg ladders with ring exchange
https://resolver.caltech.edu/CaltechAUTHORS:20120123-133929180
Authors: Mishmash, Ryan V.; Block, Matthew S.; Kaul, Ribhu K.; Sheng, D. N.; Motrunich, Olexei I.; Fisher, Matthew P. A.
Year: 2011
DOI: 10.1103/PhysRevB.84.245127
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.https://authors.library.caltech.edu/records/njgpb-ytx08Universal transport signatures of Majorana fermions in superconductor-Luttinger liquid junctions
https://resolver.caltech.edu/CaltechAUTHORS:20120716-103347564
Authors: Fidkowski, Lukasz; Alicea, Jason; Lindner, Netanel H.; Lutchyn, Roman M.; Fisher, Matthew P. A.
Year: 2012
DOI: 10.1103/PhysRevB.85.245121
One of the most promising proposals for engineering topological superconductivity and Majorana fermions employs a spin-orbit coupled nanowire subjected to a magnetic field and proximate to an s-wave superconductor. When only part of the wire's length contacts to the superconductor, the remaining conducting portion serves as a natural lead that can be used to probe these Majorana modes via tunneling. The enhanced role of interactions in one dimension dictates that this configuration should be viewed as a superconductor-Luttinger liquid junction. We investigate such junctions between both helical and spinful Luttinger liquids, and topological as well as nontopological superconductors. We determine the phase diagram for each case and show that universal low-energy transport in these systems is governed by fixed points describing either perfect normal reflection or perfect Andreev reflection. In addition to capturing (in some instances) the familiar Majorana-mediated "zero-bias anomaly" in a new framework, we show that interactions yield dramatic consequences in certain regimes. Indeed, we establish that strong repulsion removes this conductance anomaly altogether while strong attraction produces dynamically generated effective Majorana modes even in a junction with a trivial superconductor. Interactions further lead to striking signatures in the local density of states and the line shape of the conductance peak at finite voltage, and also are essential for establishing smoking-gun transport signatures of Majorana fermions in spinful Luttinger liquid junctions.https://authors.library.caltech.edu/records/qpkba-sch90Non-Fermi liquid d-wave metal phase of strongly interacting electrons
https://resolver.caltech.edu/CaltechAUTHORS:20121102-100712474
Authors: Jiang, Hong-Chen; Block, Matthew S.; Mishmash, Ryan V.; Garrison, James R.; Sheng, D. N.; Motrunich, Olexei I.; Fisher, Matthew P. A.
Year: 2013
DOI: 10.1038/nature11732
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.https://authors.library.caltech.edu/records/ehsby-7db71Phase diagram of the spin-1/2 J_1-J_2 Heisenberg model on a honeycomb lattice
https://resolver.caltech.edu/CaltechAUTHORS:20131125-113942857
Authors: Gong, Shou-Shu; Sheng, D. N.; Motrunich, Olexei I.; Fisher, Matthew P. A.
Year: 2013
DOI: 10.1103/PhysRevB.88.165138
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 0.25https://authors.library.caltech.edu/records/nm0m4-30412Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure
https://resolver.caltech.edu/CaltechAUTHORS:20140421-104643131
Authors: Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul; Nayak, Chetan; Oreg, Yuval; Stern, Ady; Berg, Erez; Shtengel, Kirill; Fisher, Matthew P. A.
Year: 2014
DOI: 10.1103/PhysRevX.4.011036
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the Z_3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that—unlike Ising anyons—allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a twofold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types, yet depending on nonuniversal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.https://authors.library.caltech.edu/records/b4q8s-8cb92Partially split Hall bar: Tunneling in the bosonic integer quantum Hall effect
https://resolver.caltech.edu/CaltechAUTHORS:20140714-134245371
Authors: Mulligan, Michael; Fisher, Matthew P. A.
Year: 2014
DOI: 10.1103/PhysRevB.89.205315
We study point-contact tunneling in the integer quantum Hall state of bosons. This symmetry-protected topological state has electrical Hall conductivity equal to 2e^2/h and vanishing thermal Hall conductivity. In contrast to the integer quantum Hall state of fermions, a point contact can have a dramatic effect on the low-energy physics. In the absence of disorder, a point contact generically leads to a partially split Hall bar geometry. We describe the resulting intermediate fixed point via the two-terminal electrical (Hall) conductance of the edge modes. Disorder along the edge, however, both restores the universality of the two-terminal conductance and helps preserve the integrity of the Hall bar within the relevant parameter regime.https://authors.library.caltech.edu/records/ebt23-93t63Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J_1−J_2 Square Heisenberg Model
https://resolver.caltech.edu/CaltechAUTHORS:20140714-131011965
Authors: Gong, Shou-Shu; Zhu, Wei; Sheng, D. N.; Motrunich, Olexei I.; Fisher, Matthew P. A.
Year: 2014
DOI: 10.1103/PhysRevLett.113.027201
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 0.5https://authors.library.caltech.edu/records/mnky6-d6k09Quantum Disentangled Liquids
https://resolver.caltech.edu/CaltechAUTHORS:20140714-160952577
Authors: Grover, Tarun; Fisher, Matthew P. A.
Year: 2014
DOI: 10.1088/1742-5468/2014/10/P10010
We propose and explore a new finite temperature phase of translationally invariant multi-component liquids which we call a 'Quantum Disentangled Liquid' (QDL) phase. We contemplate the possibility that in fluids consisting of two (or more) species of indistinguishable quantum particles with a large mass ratio, the light particles might 'localize' on the heavy particles. We give a precise, formal definition of this QDL phase in terms of the finite energy density many-particle wavefunctions. While the heavy particles are fully thermalized, for a typical fixed configuration of the heavy particles, the entanglement entropy of the light particles satisfies an area law; this implies that the light particles have not thermalized. Equivalently, but more intuitively, if the positions of all the heavy particles are measured, the projected wavefunction for the unmeasured light particles has as an area law entanglement entropy. Thus, in a QDL phase, thermal equilibration is incomplete, and the canonical assumptions of statistical mechanics are not fully operative.
The definition of the QDL phase for heavy/light particles can be readily generalized to other cases with two (or more) conserved currents, such as spin/charge in a system of spin-1/2 fermions (as in a Hubbard model). Indeed, we argue that the finite energy-density eigenstates of the t–J model will generically be in such a spin/charge QDL, although the fate of the QDL in the large U Hubbard model is uncertain. We explore the possibility of QDL in water, with the light proton degrees of freedom becoming 'localized' on the oxygen ions. While we do not presently know whether a local, generic Hamiltonian can have eigenstates of the QDL form, if not, then the non-thermal behavior discussed here will exist as an interesting crossover phenomena at a time scale that diverges as the ratio of the mass of the heavy to the light particles also diverges.https://authors.library.caltech.edu/records/dry4b-6zn80Continuous Mott transition between a metal and a quantum spin liquid
https://resolver.caltech.edu/CaltechAUTHORS:20140714-161947260
Authors: Mishmash, Ryan V.; González, Iván; Melko, Roger G.; Motrunich, Olexei I.; Fisher, Matthew P. A.
Year: 2015
DOI: 10.1103/PhysRevB.91.235140
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.https://authors.library.caltech.edu/records/95gvm-ehh34Partial breakdown of quantum thermalization in a Hubbard-like model
https://resolver.caltech.edu/CaltechAUTHORS:20170221-134248509
Authors: Garrison, James R.; Mishmash, Ryan V.; Fisher, Matthew P. A.
Year: 2017
DOI: 10.1103/PhysRevB.95.054204
We study the possible breakdown of quantum thermalization in a model of itinerant electrons on a one-dimensional chain without disorder, with both spin and charge degrees of freedom. The eigenstates of this model exhibit peculiar properties in the entanglement entropy, the apparent scaling of which is modified from a "volume law" to an "area law" after performing a partial, site-wise measurement on the system. These properties and others suggest that this model realizes a new, nonthermal phase of matter, known as a quantum disentangled liquid (QDL). The putative existence of this phase has striking implications for the foundations of quantum statistical mechanics.https://authors.library.caltech.edu/records/2qfgc-13e76Quantum indistinguishability in chemical reactions
https://resolver.caltech.edu/CaltechAUTHORS:20180430-145931994
Authors: Fisher, Matthew P. A.; Radzihovsky, Leo
Year: 2018
DOI: 10.1073/pnas.1718402115
PMCID: PMC5960291
Quantum indistinguishability plays a crucial role in many low-energy physical phenomena, from quantum fluids to molecular spectroscopy. It is, however, typically ignored in most high-temperature processes, particularly for ionic coordinates, implicitly assumed to be distinguishable, incoherent, and thus well approximated classically. We explore enzymatic chemical reactions involving small symmetric molecules and argue that in many situations a full quantum treatment of collective nuclear degrees of freedom is essential. Supported by several physical arguments, we conjecture a "quantum dynamical selection" (QDS) rule for small symmetric molecules that precludes chemical processes that involve direct transitions from orbitally nonsymmetric molecular states. As we propose and discuss, the implications of the QDS rule include (i) a differential chemical reactivity of para- and orthohydrogen, (ii) a mechanism for inducing intermolecular quantum entanglement of nuclear spins, (iii) a mass-independent isotope fractionation mechanism, (iv) an explanation of the enhanced chemical activity of "reactive oxygen species", (v) illuminating the importance of ortho-water molecules in modulating the quantum dynamics of liquid water, and (vi) providing the critical quantum-to-biochemical linkage in the nuclear spin model of the (putative) quantum brain, among others.https://authors.library.caltech.edu/records/ffjdg-ss477