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Random Matrix Ensemble for the Level Statistics of Many-Body Localization
Wouter Buijsman1, Vadim Cheianov2, Vladimir Gritsev1,3
1Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.
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.
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