Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis

Shiraishi, Naoto; Mori, Toshiyuki

doi:10.1103/physrevlett.119.030601

Cited by 307 publications

(287 citation statements)

References 56 publications

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“…where we have only assumed a self-averaging condition. Thus, comparing equations (14) and (13) we can observe that we obtain an inconsistency. We are thus lead to conclude that there are indeed correlations between the coefficients, and that equation (…”

Section: Eth and The Limitation Of The Independent Random Wave-functimentioning

confidence: 89%

Off-diagonal observable elements from random matrix theory: distributions, fluctuations, and eigenstate thermalization

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2018

New J. Phys.

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We derive the eigenstate thermalization hypothesis (ETH) from a random matrix Hamiltonian by extending the model introduced by Deutsch (1991 Phys. Rev. A 43 2046). We approximate the coupling between a subsystem and a many-body environment by means of a random Gaussian matrix. We show that a common assumption in the analysis of quantum chaotic systems, namely the treatment of eigenstates as independent random vectors, leads to inconsistent results. However, a consistent approach to the ETH can be developed by introducing an interaction between random wave-functions that arises as a result of the orthonormality condition. This approach leads to a consistent form for off-diagonal matrix elements of observables. From there we obtain the scaling of time-averaged fluctuations of generic observables with system size for which we calculate an analytic form in terms of the inverse participation ratio. The analytic results are compared to exact diagonalizations of a quantum spin chain for different physical observables in multiple parameter regimes.

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Section: Eth and The Limitation Of The Independent Random Wave-functimentioning

confidence: 89%

Off-diagonal observable elements from random matrix theory: distributions, fluctuations, and eigenstate thermalization

Nation

Porras

2018

New J. Phys.

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“…Thus, while Hamiltonians of the form (2.13a) and (2.15) can be constructed for each tower of states individually, it is apparently not possible to embed both towers of states in the ground state manifold of a local Hamiltonian, or among the excited states of another Hamiltonian using the embedding technique of Ref. [32]. Despite this, both towers of states appear as eigenstates of the local Hamiltonian (2.1).…”

Section: Scarred Eigenstates As Ground Statesmentioning

confidence: 99%

Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals

2020

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We construct a set of exact, highly excited eigenstates for a nonintegrable spin-1/2 model in one dimension. These states provide a new solvable example of quantum many-body scars: their subvolume-law entanglement and equal energy spacing allow for infinitely long-lived coherent oscillations of local observables following a suitable quantum quench. While previous works on scars have interpreted such oscillations in terms of the precession of an emergent macroscopic SU(2) spin, the present model evades this description due to a set of emergent kinetic constraints in the scarred eigenstates that are absent in the underlying Hamiltonian. We also analyze the set of initial states that give rise to periodic revivals. Remarkably, a subset of these initial states coincides with the family of area-law entangled Rokhsar-Kivelson states shown by Lesanovsky to be exact ground states for a class of models relevant to experiments on Rydberg-blockaded atomic lattices. arXiv:1910.11350v1 [cond-mat.str-el]

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“…Models of this form generically contain eigenstates embedded near the center of the spectrum. 29 There is no guarantee embedded states are equidistant in energy and may even be degenerate, such that this scheme can produce models which do not exhibit perfect wavefunction revivals. We note that, for periodic boundary conditions, the PXP model, introduced in Sec.…”

Section: A Projector Embeddingmentioning

confidence: 99%

Quantum scars as embeddings of weakly broken Lie algebra representations

2020

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We present an interpretation of scar states and quantum revivals as weakly "broken" representations of Lie algebras spanned by a subset of eigenstates of a many-body quantum system. We show that the PXP model, describing strongly-interacting Rydberg atoms, supports a "loose" embedding of multiple su(2) Lie algebras corresponding to distinct families of scarred eigenstates. Moreover, we demonstrate that these embeddings can be made progressively more accurate via an iterative process which results in optimal perturbations that stabilize revivals from arbitrary charge density wave product states, |Zn , including ones that show no revivals in the unperturbed PXP model. We discuss the relation between the loose embeddings of Lie algebras present in the PXP model and recent exact constructions of scarred states in related models. arXiv:2001.08232v1 [cond-mat.str-el]

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Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis

Cited by 307 publications

References 56 publications

Off-diagonal observable elements from random matrix theory: distributions, fluctuations, and eigenstate thermalization

Off-diagonal observable elements from random matrix theory: distributions, fluctuations, and eigenstate thermalization

Quantum many-body scar states with emergent kinetic constraints and finite-entanglement revivals

Quantum scars as embeddings of weakly broken Lie algebra representations

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