Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition
Abstract
We employ singular value decomposition to study the eigenvalue spectrums of random spin systems. It's shown the singular values $\lambda_k$ of the sample matrix in the ergodic phase contain two branches that both follow powerlaw behavior but with different power exponents $\alpha$. By analyzing the singular vectors, it is verified the higher part of $\lambda_k$ with $k>k_{\text{Th}}$ are universal that follows random matrix theory, where $k_{\text{Th}}$ estimates the Thouless energy. We further demonstrate that $\alpha$ corresponds only to the exponential part of the level spacing distribution while is insensitive to the level repulsion, or equivalently the system's symmetry. Consequently, the power exponent $\alpha$ gives an underestimation for the manybody localization transition point, which, however, reveals the Griffiths regime in a transparent way.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.05120
 Bibcode:
 2021arXiv211005120R
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 7 pages, 5 figures