https://doi.org/10.1140/epjp/s13360-024-05537-w
Regular Article
Analyzing the eigenvalue statistics of random spin system via modeling random matrix model
School of Sciences, Hangzhou Dianzi University, 310018, Hangzhou, China
Received:
9
February
2024
Accepted:
4
August
2024
Published online:
12
August
2024
This work explores the possibility of describing the eigenvalue statistics of a physical model with ergodic to many-body localization transition by a modeling random matrix model. Specifically, we employ the power-law random banded matrix ensemble (PRBM) to fit the eigenvalue statistics of a random spin system. For the short-range level statistics, we study the conventional spacing ratio distributions. As to the long-range level correlations, we employ the techniques of singular value decomposition that avoid the unfolding procedure. The results show that PRBM is capable of reproducing the short-range level statistics of the physical model over the whole phase diagram with a high accuracy, and the long-range part displays non-negligible mismatch only in the transition regime, which is attributed to the sample-to-sample fluctuation that drives the phase transition in the physical model while is absent in the PRBM.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
