A Complex Network Analysis on The Eigenvalue Spectra of Random Spin Systems
arXiv:2311.04665 · doi:10.1016/j.physa.2024.129572
Abstract
Recent works have established a novel viewpoint that treats the eigenvalue spectra of disordered quantum systems as time-series, and corresponding algorithms 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's shown 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.
arXiv comment14 pages, 4 figures
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