Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis

Naoto Shiraishi and Takashi Mori
Phys. Rev. Lett. 119, 030601 – Published 21 July 2017
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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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  • Received 4 February 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.030601

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Naoto Shiraishi

  • Department of Physics, Keio University, 3-14-1 Hiyoshi, Yokohama 223-8522, Japan

Takashi Mori

  • Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

Comments & Replies

Comment on “Systematic Construction of Counterexamples to the Eigenstate Thermalization Hypothesis”

Rubem Mondaini, Krishnanand Mallayya, Lea F. Santos, and Marcos Rigol
Phys. Rev. Lett. 121, 038901 (2018)

Shiraishi and Mori Reply

Naoto Shiraishi and Takashi Mori
Phys. Rev. Lett. 121, 038902 (2018)

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Issue

Vol. 119, Iss. 3 — 21 July 2017

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