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.

arXiv comment7 pages, 4 figures

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• Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition
• Power-Law Random Banded Matrix Ensemble as the Effective Model for Many-Body Localization Transition
• Random Matrix Model for Eigenvalue Statistics in Random Spin Systems
• Tracking locality in time evolution of disordered systems
• Universal scaling of higher-order spacing ratios in Gaussian random matrices
• A Complex Network Analysis on The Eigenvalue Spectra of Random Spin Systems