A complex network analysis on the eigenvalue spectra of random spin systems

Qiaomu Xue and Wenjia Rao

Physica A: Statistical Mechanics and its Applications, 2024, vol. 636, issue C

Abstract: Recent works have established a novel viewpoint that treats the eigenvalue spectra of disordered quantum systems as time-series, and corresponding algorithm such as singular-value-decomposition has proven its advantage in studying subtle physical quantities like Thouless energy and non-ergodic extended regime. On the other hand, algorithms from complex networks have long been known as a powerful tool to study highly nonlinear time-series. In this work, we combine these two ideas together. Using the particular algorithm called visibility graph (VG) that transforms the eigenvalue spectra of a random spin system into complex networks, it is shown that the degree distribution of the resulting network is capable of signaturing the eigenvalue evolution during the thermal to many-body localization transition, and the networks in the thermal phase have a small-world structure. We further show these results are robust even when the eigenvalues are incomplete with missing levels, which reveals the advantage of the VG algorithm.

Keywords: Complex network; Visibility graph; Eigenvalue spectrum; Many-body localization; Random spin system (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:636:y:2024:i:c:s0378437124000803

DOI: 10.1016/j.physa.2024.129572

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