[ { "id": "authors:g73gm-h9f87", "collection": "authors", "collection_id": "g73gm-h9f87", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200709-135402210", "type": "article", "title": "Slow thermalization of exact quantum many-body scar states under perturbations", "author": [ { "family_name": "Lin", "given_name": "Cheng-Ju", "orcid": "0000-0001-7898-0211", "clpid": "Lin-Cheng-Ju" }, { "family_name": "Chandran", "given_name": "Anushya", "orcid": "0000-0002-2046-1379", "clpid": "Chandran-A" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-O-I" } ], "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\u2217\u223cO(\u03bb^(\u22121/(1+d))), where d is the spatial dimension of the system and \u03bb is the perturbation strength.", "doi": "10.1103/physrevresearch.2.033044", "issn": "2643-1564", "publisher": "American Physical Society", "publication": "Physical Review Research", "publication_date": "2020-07", "series_number": "3", "volume": "2", "issue": "3", "pages": "Art. No. 033044" }, { "id": "authors:5wk3b-1yk90", "collection": "authors", "collection_id": "5wk3b-1yk90", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200518-131230068", "type": "article", "title": "Unified structure for exact towers of scar states in the Affleck-Kennedy-Lieb-Tasaki and other models", "author": [ { "family_name": "Mark", "given_name": "Daniel K.", "orcid": "0000-0002-5017-5218", "clpid": "Mark-D-K" }, { "family_name": "Lin", "given_name": "Cheng-Ju", "orcid": "0000-0001-7898-0211", "clpid": "Lin-Cheng-Ju" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-O-I" } ], "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.", "doi": "10.1103/physrevb.101.195131", "issn": "2469-9950", "publisher": "American Physical Society", "publication": "Physical Review B", "publication_date": "2020-05-15", "series_number": "19", "volume": "101", "issue": "19", "pages": "Art. No. 195131" }, { "id": "authors:mngxa-qq619", "collection": "authors", "collection_id": "mngxa-qq619", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191223-160336506", "type": "article", "title": "Exact eigenstates in the Lesanovsky model, proximity to integrability and the PXP model, and approximate scar states", "author": [ { "family_name": "Mark", "given_name": "Daniel K.", "orcid": "0000-0002-5017-5218", "clpid": "Mark-D-K" }, { "family_name": "Lin", "given_name": "Cheng-Ju", "orcid": "0000-0001-7898-0211", "clpid": "Lin-Cheng-Ju" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-O-I" } ], "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.", "doi": "10.1103/PhysRevB.101.094308", "issn": "2469-9950", "publisher": "American Physical Society", "publication": "Physical Review B", "publication_date": "2020-03-01", "series_number": "9", "volume": "101", "issue": "9", "pages": "Art. No. 094308" }, { "id": "authors:xh6bj-gf612", "collection": "authors", "collection_id": "xh6bj-gf612", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200303-083407096", "type": "monograph", "title": "Unified structure for exact towers of scar states in the AKLT and other models", "author": [ { "family_name": "Mark", "given_name": "Daniel K.", "clpid": "Mark-D-K" }, { "family_name": "Lin", "given_name": "Cheng-Ju", "orcid": "0000-0001-7898-0211", "clpid": "Lin-Cheng-Ju" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-O-I" } ], "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.", "doi": "10.48550/arXiv.2001.03839", "publisher": "arXiv", "publication_date": "2020-01-12" }, { "id": "authors:4b2fy-j4889", "collection": "authors", "collection_id": "4b2fy-j4889", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181203-095532141", "type": "article", "title": "Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain", "author": [ { "family_name": "Lin", "given_name": "Cheng-Ju", "orcid": "0000-0001-7898-0211", "clpid": "Lin-Cheng-Ju" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-O-I" } ], "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 = \u00b1\u221a2). 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.", "doi": "10.1103/physrevlett.122.173401", "issn": "0031-9007", "publisher": "American Physical Society", "publication": "Physical Review Letters", "publication_date": "2019-05-03", "series_number": "17", "volume": "122", "issue": "17", "pages": "Art. No. 173401" }, { "id": "authors:qe72a-98216", "collection": "authors", "collection_id": "qe72a-98216", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180821-145330708", "type": "article", "title": "Out-of-time-ordered correlators in short-range and long-range hard-core boson models and Luttinger liquid model", "author": [ { "family_name": "Lin", "given_name": "Cheng-Ju", "orcid": "0000-0001-7898-0211", "clpid": "Lin-Cheng-Ju" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-O-I" } ], "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.", "doi": "10.1103/PhysRevB.98.134305", "issn": "2469-9950", "publisher": "American Physical Society", "publication": "Physical Review B", "publication_date": "2018-10-01", "series_number": "13", "volume": "98", "issue": "13", "pages": "Art. No. 134305" }, { "id": "authors:vdp0v-e8390", "collection": "authors", "collection_id": "vdp0v-e8390", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180418-093907947", "type": "article", "title": "Out-of-time-ordered correlators in a quantum Ising chain", "author": [ { "family_name": "Lin", "given_name": "Cheng-Ju", "orcid": "0000-0001-7898-0211", "clpid": "Lin-Cheng-Ju" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-O-I" } ], "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^(\u22121) 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^(\u22121/4) 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.", "doi": "10.1103/PhysRevB.97.144304", "issn": "2469-9950", "publisher": "American Physical Society", "publication": "Physical Review B", "publication_date": "2018-04-01", "series_number": "14", "volume": "97", "issue": "14", "pages": "Art. no. 144304" }, { "id": "authors:cj6j8-b1858", "collection": "authors", "collection_id": "cj6j8-b1858", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171004-144618632", "type": "article", "title": "Explicit construction of quasiconserved local operator of translationally invariant nonintegrable quantum spin chain in prethermalization", "author": [ { "family_name": "Lin", "given_name": "Cheng-Ju", "orcid": "0000-0001-7898-0211", "clpid": "Lin-Cheng-Ju" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-O-I" } ], "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.", "doi": "10.1103/PhysRevB.96.214301", "issn": "2469-9950", "publisher": "American Physical Society", "publication": "Physical Review B", "publication_date": "2017-12-01", "series_number": "21", "volume": "96", "issue": "21", "pages": "Art. No. 214301" }, { "id": "authors:mj76j-vc952", "collection": "authors", "collection_id": "mj76j-vc952", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161212-141040765", "type": "article", "title": "Quasiparticle explanation of the weak-thermalization regime under quench in a nonintegrable quantum spin chain", "author": [ { "family_name": "Lin", "given_name": "Cheng-Ju", "orcid": "0000-0001-7898-0211", "clpid": "Lin-Cheng-Ju" }, { "family_name": "Motrunich", "given_name": "Olexei I.", "orcid": "0000-0001-8031-0022", "clpid": "Motrunich-O-I" } ], "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 [Ba\u00f1uls, 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^(\u22123/2) 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.", "doi": "10.1103/PhysRevA.95.023621", "issn": "2469-9926", "publisher": "American Physical Society", "publication": "Physical Review A", "publication_date": "2017-02", "series_number": "2", "volume": "95", "issue": "2", "pages": "Art. No. 023621" }, { "id": "authors:qx06x-d8q90", "collection": "authors", "collection_id": "qx06x-d8q90", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160812-111950839", "type": "article", "title": "Signatures of strong correlation effects in resonant inelastic x-ray scattering studies on cuprates", "author": [ { "family_name": "Li", "given_name": "Wan-Ju", "clpid": "Li-Wan-Ju" }, { "family_name": "Lin", "given_name": "Cheng-Ju", "orcid": "0000-0001-7898-0211", "clpid": "Lin-Cheng-Ju" }, { "family_name": "Lee", "given_name": "Ting-Hui", "clpid": "Lee-Ting-Hui" } ], "abstract": "Recently, spin excitations in doped cuprates have been measured using resonant inelastic x-ray scattering. The paramagnon dispersions show the large hardening effect in the electron-doped systems and seemingly doping independence in the hole-doped systems, with the energy scales comparable to that of the antiferromagnetic (AFM) magnons. This anomalous hardening effect and the lack of softening were partially explained by using the strong-coupling t\u2212J model but with a three-site term [Nat. Commun. 5, 3314 (2014)], although the hardening effect is already present even without the latter. By considering the t\u2212t\u2032\u2212t\"\u2212J model and using the slave-boson mean-field theory, we obtain, via the spin-spin susceptibility, the spin excitations in qualitative agreement with the experiments. The doping-dependent bandwidth due to the strong correlation physics is the origin of the hardening effect. We also show that dispersions in the AFM regime, different from those in the paramagnetic (PM) regime, hardly vary with dopant density. These excitations are mainly collective in nature instead of particle-hole-like. We further discuss the interplay and different contributions of these two kinds of excitations in the PM phase and show that the dominance of the collective excitation increases with decreasing dopant concentrations.", "doi": "10.1103/PhysRevB.94.075127", "issn": "2469-9950", "publisher": "American Physical Society", "publication": "Physical Review B", "publication_date": "2016-08-15", "series_number": "7", "volume": "94", "issue": "7", "pages": "Art. No. 075127" } ]