TY - JOUR
T1 - Random Matrix Ensemble for the Level Statistics of Many-Body Localization
AU - Buijsman, Wouter
AU - Cheianov, Vadim
AU - Gritsev, Vladimir
N1 - Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/5/10
Y1 - 2019/5/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85065774505&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.122.180601
DO - 10.1103/PhysRevLett.122.180601
M3 - Article
C2 - 31144897
AN - SCOPUS:85065774505
SN - 0031-9007
VL - 122
JO - Physical Review Letters
JF - Physical Review Letters
IS - 18
M1 - 180601
ER -