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arXiv · 2410.12430

Renormalization-Group Analysis of the Many-Body Localization Transition in the Random-Field XXZ Chain

Jacopo Niedda·Giacomo Bracci-Testasecca·Giuseppe Magnifico·Federico Balducci·Carlo Vanoni·Antonello Scardicchio
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Abstract

We analyze the spectral properties of the Heisenberg spin-1/2 chain with random fields in light of recent works of the renormalization-group flow of the Anderson model in infinite dimension. We reconstruct the beta function of the order parameter from the numerical data, and show that it does not admit a one-parameter scaling form and a simple Wilson-Fisher fixed point. Rather, it is compatible with a two-parameter, Berezinskii-Kosterlitz-Thouless-like flow with a line of fixed points (the many-body localized phase), which terminates into the localization transition critical point. Therefore, we argue that previous studies, which assumed the existence of an isolated Wilson- Fisher fixed point and performed one-parameter finite-size scaling analysis, could not explain the numerical data in a coherent way.

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Jacopo Niedda, Giacomo Bracci-Testasecca, Giuseppe Magnifico, Federico Balducci, Carlo Vanoni, Antonello Scardicchio. 2024-10-16. Renormalization-Group Analysis of the Many-Body Localization Transition in the Random-Field XXZ Chain. https://doi.org/10.1103/gcwf-jdlr

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