Random Matrix Ensemble for the Level Statistics of Many-Body Localization

Wouter Buijsman, Vadim Cheianov, Vladimir Gritsev

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

We numerically study the level statistics of the Gaussian β ensemble. These statistics generalize Wigner-Dyson level statistics from the discrete set of Dyson indices β=1, 2, 4 to the continuous range 0<β<∞. The Gaussian β ensemble covers Poissonian level statistics for β→0, and provides a smooth interpolation between Poissonian and Wigner-Dyson level statistics. We establish the physical relevance of the level statistics of the Gaussian β ensemble by showing near-perfect agreement with the level statistics of a paradigmatic model in studies on many-body localization over the entire crossover range from the thermal to the many-body localized phase. In addition, we show similar agreement for a related Hamiltonian with broken time-reversal symmetry.

Original languageEnglish
Article number180601
JournalPhysical Review Letters
Volume122
Issue number18
DOIs
StatePublished - 10 May 2019
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy

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