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

被引：53

作者：

Buijsman, Wouter ^{[1
,2
]}

Cheianov, Vadim ^{[3
,4
]}

Gritsev, Vladimir ^{[1
,2
,5
]}

机构：

[1] Univ Amsterdam, Inst Theoret Phys Amsterdam, Sci Pk 904, NL-1098 XH Amsterdam, Netherlands

[2] Univ Amsterdam, Delta Inst Theoret Phys, Sci Pk 904, NL-1098 XH Amsterdam, Netherlands

[3] Leiden Univ, Inst Lorentz, POB 9506, NL-2300 RA Leiden, Netherlands

[4] Leiden Univ, Delta Inst Theoret Phys, POB 9506, NL-2300 RA Leiden, Netherlands

[5] Russian Quantum Ctr, Moscow 143025, Russia

来源：

PHYSICAL REVIEW LETTERS | 2019年 / 122卷 / 18期

关键词：

TRANSITION REGION; BETA-HERMITE; CHAOS; INTEGRABILITY; UNIVERSALITY; SPECTRUM; MODELS;

D O I：

10.1103/PhysRevLett.122.180601

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We numerically study the level statistics of the Gaussian beta ensemble. These statistics generalize Wigner-Dyson level statistics from the discrete set of Dyson indices beta = 1, 2, 4 to the continuous range 0 < beta < infinity. The Gaussian beta ensemble covers Poissonian level statistics for beta -> 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 beta 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.

引用

页数：6

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