Quantum Ergodicity in the Many-Body Localization Problem

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

doi:10.1103/physrevlett.127.030601

Quantum Ergodicity in the Many-Body Localization Problem

Journal Article · Thu Jul 15 00:00:00 EDT 2021 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.127.030601· OSTI ID:1852162

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Ministerio da Ciencia, Tecnologia e Inovacao (MCTI), Rio de Janiero (Brazil); OSTI
Kyoto Univ. (Japan)
Univ. of Cologne (Germany)
Princeton Univ., NJ (United States)
Ministerio da Ciencia, Tecnologia e Inovacao (MCTI), Rio de Janiero (Brazil)

Here, 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.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC); German Research Foundation (DFG); Japan Society for the Promotion of Science (JSPS)

Grant/Contract Number:: SC0016244

OSTI ID:: 1852162

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 3 Vol. 127; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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