Critical Level Statistics at the Many-Body Localization Transition Region

Abstract

We study the critical level statistics at the many-body localization (MBL) transition region in random spin systems. By employing the inter-sample randomness as indicator, we manage to locate the MBL transition point in both orthogonal and unitary models. We further count the $n$-th order gap ratio distributions at the transition region up to $n=4$, and find they fit well with the short-range plasma model (SRPM) with inverse temperature $\beta =1$ for orthogonal model and $\beta =2$ for unitary. These critical level statistics are argued to be universal by comparing results from systems both with and without total $S_z$ conservation. We also point out that these critical distributions can emerge from the spectrum of a Poisson ensemble, which indicates the thermal-MBL transition point is more affected by the MBL phase rather than thermal phase.

7 pages, 4 figures

References in corpus (7)

• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Many-Body Localization in a Quasiperiodic System
• Anomalous diffusion and Griffiths effects near the many-body localization transition
• Quantum quenches in the many-body localized phase
• Higher-order level spacings in random matrix theory based on Wigner's conjecture