Eigenstate thermalization in the two-dimensional transverse field Ising model

Mondaini, Rubem; Fratus, Keith R.; Srednicki, Mark; Rigol, Marcos

doi:10.1103/physreve.93.032104

Cited by 140 publications

(131 citation statements)

References 45 publications

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“…Questions about ETH in systems in two or more dimensions, such as the transverse-field Ising model on the square lattice [14][15][16], are of great interest but challenging due to the rapid increase of the Hilbert-space dimension with system size. Second, the Hilbert space of the QDM is spanned by dimer configurations subject to strong local constraints.…”

Section: Introductionmentioning

confidence: 99%

“…To provide a more quantitative picture, we employ an approach that has proved useful in previous studies [14,17] by looking at fluctuations between the diagonal matrix elements in adjacent energy eigenstates. We first sort all the eigenstates by energy and then calculate the difference of diagonal matrix elements between adjacent eigenstates,…”

Section: A Eth For the Square Qdmmentioning

confidence: 99%

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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%

Section: A Eth For the Square Qdmmentioning

confidence: 99%

Eigenstate thermalization hypothesis in quantum dimer models

Lan

Powell

2017

Phys. Rev. B

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“…Many numerical simulations report that the ETH is valid if the Hamiltonian of a many-body quantum system satisfies the following three conditions: (i) translation invariance (in particular, no localization [37]), (ii) no local conserved quantity, and (iii) local interactions [23,24,30,[41][42][43][44][45][46]. Here, the word local stands for both few-body and short-range.…”

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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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“…In particular, the expectation values of few-body operators within individual eigenstates coincide with the thermal ones. There is a growing body of theoretical and numerical work supporting this hypothesis [45][46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Many-body localization beyond eigenstates in all dimensions

et al. 2016

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Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual eigenstates capture this breakdown of thermalization at finite size. We show that this belief is false in general and that a MBL system can exhibit the eigenstate properties of a thermalizing system. We propose that localized approximately conserved operators (l * -bits) underlie localization in such systems. In dimensions d > 1, we further argue that the existing MBL phenomenology is unstable to boundary effects and gives way to l * -bits. Physical consequences of l * -bits include the possibility of an eigenstate phase transition within the MBL phase unrelated to the dynamical transition in d = 1 and thermal eigenstates at all parameters in d > 1. Near-term experiments in ultra-cold atomic systems and numerics can probe the dynamics generated by boundary layers and emergence of l * -bits.

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Eigenstate thermalization in the two-dimensional transverse field Ising model

Cited by 140 publications

References 45 publications

Eigenstate thermalization hypothesis in quantum dimer models

Eigenstate thermalization hypothesis in quantum dimer models

Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis

Many-body localization beyond eigenstates in all dimensions

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