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

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  • Xue, Qiaomu
  • Rao, Wenjia

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.

Suggested Citation

  • Xue, Qiaomu & Rao, Wenjia, 2024. "A complex network analysis on the eigenvalue spectra of random spin systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 636(C).
    • Handle: RePEc:eee:phsmap:v:636:y:2024:i:c:s0378437124000803
    DOI: 10.1016/j.physa.2024.129572
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    References listed on IDEAS

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    1. Yang, Yue & Yang, Huijie, 2008. "Complex network-based time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1381-1386.
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