Quantum Ergodicity in the Many-Body Localization Problem

Felipe Monteiro, Masaki Tezuka, Alexander Altland, David A. Huse, and Tobias Micklitz

Phys. Rev. Lett. 127, 030601 – Published 15 July 2021

Abstract

We generalize Page’s result on the entanglement entropy of random pure states to the many-body eigenstates of realistic disordered many-body systems subject to long-range interactions. This extension leads to two principal conclusions: first, for increasing disorder the “shells” of constant energy supporting a system’s eigenstates fill only a fraction of its full Fock space and are subject to intrinsic correlations absent in synthetic high-dimensional random lattice systems. Second, in all regimes preceding the many-body localization transition individual eigenstates are thermally distributed over these shells. These results, corroborated by comparison to exact diagonalization for an SYK model, are at variance with the concept of “nonergodic extended states” in many-body systems discussed in the recent literature.

Received 23 December 2020
Revised 9 April 2021
Accepted 28 May 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.030601

Physics Subject Headings (PhySH)

Entanglement entropy Many-body localization Quantum entanglement

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Felipe Monteiro ¹, Masaki Tezuka ², Alexander Altland ³, David A. Huse ⁴, and Tobias Micklitz ¹

¹Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil
²Department of Physics, Kyoto University, Kyoto 606-8502, Japan
³Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Cologne, Germany
⁴Department of Physics, Princeton University, Princeton, New Jersey 08544, USA