Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries

Hamazaki, Ryusuke; Ikeda, Tatsuhiko; Ueda, Masahito

doi:10.1103/physreve.93.032116

Cited by 29 publications

(27 citation statements)

References 90 publications

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“…By contrast, for nonbipartite lattices, the winding numbers can be defined only modulo 2, and there are four sectors defined by a pair of Z 2 invariants [24,25]. Noting the effect of topological blocking on quench dynamics [26] and recalling the case of integrable models, where the extensive number of conserved quantities invalidates ETH, it is natural to ask whether the existence of these topological invariants will influence ETH in the QDM [18].…”

Section: Introductionmentioning

confidence: 99%

Eigenstate thermalization hypothesis in quantum dimer models

Lan

Powell

2017

Phys. Rev. B

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We use exact diagonalization to study the eigenstate thermalization hypothesis (ETH) in the quantum dimer model on the square and triangular lattices. Due to the nonergodicity of the local plaquette-flip dynamics, the Hilbert space, which consists of highly constrained close-packed dimer configurations, splits into sectors characterized by topological invariants. We show that this has important consequences for ETH: We find that ETH is clearly satisfied only when each topological sector is treated separately, and only for moderate ratios of the potential and kinetic terms in the Hamiltonian. By contrast, when the spectrum is treated as a whole, ETH breaks down on the square lattice and, apparently, also on the triangular lattice. These results demonstrate that quantum dimer models have interesting thermalization dynamics.

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Section: Introductionmentioning

confidence: 99%

Eigenstate thermalization hypothesis in quantum dimer models

Lan

Powell

2017

Phys. Rev. B

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“…Interestingly, all known examples not satisfying the ETH violates at least one of (i)-(iii). Integrable systems [24,30,41,42] and systems with local symmetries [47] violate (ii), and systems with Anderson localization [48,49] or many-body localization [50,51] violate (i). It is noteworthy that these examples do not thermalize.…”

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confidence: 99%

Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis

2017

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We propose a general method to embed target states into the middle of the energy spectrum of a many-body Hamiltonian as its energy eigenstates. Employing this method, we construct a translationally-invariant local Hamiltonian with no local conserved quantities, which does not satisfy the eigenstate thermalization hypothesis. The absence of eigenstate thermalization for target states is analytically proved and numerically demonstrated. In addition, numerical calculations of two concrete models also show that all the energy eigenstates except for the target states have the property of eigenstate thermalization, from which we argue that our models thermalize after a quench even though they does not satisfy the eigenstate thermalization hypothesis.

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“…Counterexamples are the driven Rabi model56 or a non-integrable model of hard-core bosons on connected triangular lattices57. For the latter one it has been shown that the applicability of the CGE to the stationary state depends on the symmetries in the system: In case of an extensive number of local symmetries the GGE has to be applied rather than the CGE.…”

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confidence: 99%

Test of quantum thermalization in the two-dimensional transverse-field Ising model

Blaß¹,

Rieger²

2016

Sci Rep

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We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems.

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Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries

Cited by 29 publications

References 90 publications

Eigenstate thermalization hypothesis in quantum dimer models

Eigenstate thermalization hypothesis in quantum dimer models

Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis

Test of quantum thermalization in the two-dimensional transverse-field Ising model

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