Eigenstate thermalization hypothesis in quantum dimer models

Lan, Zhihao; Powell, Stephen

doi:10.1103/physrevb.96.115140

Cited by 34 publications

(29 citation statements)

References 36 publications

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“…(5) is related to a class of models that represent interactions between fundamental excitations in topological phases of matter in two dimensions. 33,76,[78][79][80][81][82][83] A wide class of such phases are the fractional quantum Hall states, in which electrons fractionalize into Abelian or non-Abelian anyons. In particular, in a ν = 12/5 fractional quantum Hall state, the fundamental excitation is a Fibonacci anyon τ .…”

Section: Discussion and Outlookmentioning

confidence: 99%

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

et al. 2018

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Recent realization of a kinetically-constrained chain of Rydberg atoms by Bernien et al. [Nature 551, 579 (2017)] resulted in the observation of unusual revivals in the many-body quantum dynamics. In our previous work, Turner et al. [arXiv:1711.03528], such dynamics was attributed to the existence of "quantum scarred" eigenstates in the many-body spectrum of the experimentally realized model. Here we present a detailed study of the eigenstate properties of the same model. We find that the majority of the eigenstates exhibit anomalous thermalization: the observable expectation values converge to their Gibbs ensemble values, but parametrically slower compared to the predictions of the eigenstate thermalization hypothesis (ETH). Amidst the thermalizing spectrum, we identify non-ergodic eigenstates that strongly violate the ETH, whose number grows polynomially with system size. Previously, the same eigenstates were identified via large overlaps with certain product states, and were used to explain the revivals observed in experiment. Here we find that these eigenstates, in addition to highly atypical expectation values of local observables, also exhibit sub-thermal entanglement entropy that scales logarithmically with the system size. Moreover, we identify an additional class of quantum scarred eigenstates, and discuss their manifestations in the dynamics starting from initial product states. We use forward scattering approximation to describe the structure and physical properties of quantum-scarred eigenstates. Finally, we discuss the stability of quantum scars to various perturbations. We observe that quantum scars remain robust when the introduced perturbation is compatible with the forward scattering approximation. In contrast, the perturbations which most efficiently destroy quantum scars also lead to the restoration of "canonical" thermalization. arXiv:1806.10933v2 [cond-mat.quant-gas]

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Section: Discussion and Outlookmentioning

confidence: 99%

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

et al. 2018

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“…Evidence for the weak ETH has been seen in many nonintegrable systems, primarily through exact diagonalization of small systems. 10,12,13,15,[17][18][19][20][21][22][23] Generally the rare states are observed at the very edges of the spectrum, which is not entirely surprising with many cases of low energy emergent integrability being known (see, e.g., Ref. 24 ).…”

Section: Introductionmentioning

confidence: 86%

“…Similar sharpening of the distribution of EEVs, and improved agreement with the MCE, is observed in exact diagonalization of lattice models (see, e.g., Refs. 10,12,15,18,20,22,23,25,41 ). We note that here the agreement is particularly clear compared to lattice calculations, as TSMs allow us to access many states in the low-energy spectrum at relatively large system size.…”

Section: Finite Size Scaling Analysismentioning

confidence: 99%

Signatures of rare states and thermalization in a theory with confinement

2019

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There is a dichotomy in the nonequilibrium dynamics of quantum many body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains extensive memory about the initial state of the system. On the other hand, in generic systems such expectation values relax to stationary values described by the thermal ensemble, fixed solely by the energy of the state. At the heart of understanding this dichotomy is the eigenstate thermalization hypothesis (ETH): individual eigenstates in nonintegrable systems are thermal, in the sense that expectation values agree with the thermal prediction at a temperature set by the energy of the eigenstate. In systems where ETH is violated, thermalization can be avoided. Thus establishing the range of validity of ETH is crucial in understanding whether a given quantum system thermalizes. Here we study a simple model with confinement, the quantum Ising chain with a longitudinal field, in which ETH is violated. Despite an absence of integrability, there exist rare (nonthermal) states that persist far into the spectrum. These arise as a direct consequence of confinement: pairs of particles are confined, forming new 'meson' excitations whose energy can be extensive in the system size. We show that such states are nonthermal in both the continuum and in the low-energy spectrum of the corresponding lattice model. We highlight that the presence of such states within the spectrum has important consequences, with certain quenches leading to an absence of thermalization and local observables evolving anomalously. arXiv:1808.10782v2 [cond-mat.str-el]

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“…So far, the ETH has been verified for a wide number of lattice models such as nonintegrable spin-1/2 chains [23][24][25][26][27][28][29][30][31][32][33], ladders [26,[34][35][36] and square lattices [37][38][39], interacting spinless fermions [40,41], Bose-Hubbard [26,42] and Fermi-Hubbard chains [43], dipolar hard-core bosons [44], quantum dimer models [45] and Fibonacci anyons [46]. In these examples, mostly, direct two-body interactions in systems of either spins, fermions or bosons are responsible for rendering the system ergodic.…”

Section: Introductionmentioning

confidence: 95%

Eigenstate thermalization and quantum chaos in the Holstein polaron model

et al. 2019

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The eigenstate thermalization hypothesis (ETH) is a successful theory that provides sufficient criteria for ergodicity in quantum many-body systems. Most studies were carried out for Hamiltonians relevant for ultracold quantum gases and single-component systems of spins, fermions, or bosons. The paradigmatic example for thermalization in solid-state physics are phonons serving as a bath for electrons. This situation is often viewed from an open-quantum system perspective. Here, we ask whether a minimal microscopic model for electron-phonon coupling is quantum chaotic and whether it obeys ETH, if viewed as a closed quantum system. Using exact diagonalization, we address this question in the framework of the Holstein polaron model. Even though the model describes only a single itinerant electron, whose coupling to dispersionless phonons is the only integrability-breaking term, we find that the spectral statistics and the structure of Hamiltonian eigenstates exhibit essential properties of the corresponding random-matrix ensemble. Moreover, we verify the ETH ansatz both for diagonal and offdiagonal matrix elements of typical phonon and electron observables, and show that the ratio of their variances equals the value predicted from random-matrix theory.

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Eigenstate thermalization hypothesis in quantum dimer models

Cited by 34 publications

References 36 publications

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

Signatures of rare states and thermalization in a theory with confinement

Eigenstate thermalization and quantum chaos in the Holstein polaron model

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