Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis

Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis 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 do not satisfy the eigenstate thermalization hypothesis. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review Letters American Physical Society (APS)

Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis

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Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis

Abstract

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 do not satisfy the eigenstate thermalization hypothesis.
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Publisher
The American Physical Society
Copyright
Copyright © © 2017 American Physical Society
ISSN
0031-9007
eISSN
1079-7114
D.O.I.
10.1103/PhysRevLett.119.030601
Publisher site
See Article on Publisher Site

Abstract

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 do not satisfy the eigenstate thermalization hypothesis.

Journal

Physical Review LettersAmerican Physical Society (APS)

Published: Jul 21, 2017

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