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Renormalization group analysis of the many-body localization transition in the random-field XXZ chain

Jacopo Niedda1,*, Giacomo Bracci Testasecca2,3,†, Giuseppe Magnifico4,5, Federico Balducci6, Carlo Vanoni2,7, and Antonello Scardicchio1,3

  • *Contact author: jniedda@ictp.it
  • †Contact author: gbraccit@sissa.it
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Phys. Rev. B 112, 144201 – Published 1 October, 2025

DOI: https://doi.org/10.1103/gcwf-jdlr

Abstract

The spectral properties of the Heisenberg spin-1/2 chain with random fields are analyzed in light of recent works on the renormalization-group flow of the Anderson model in infinite dimension. We reconstruct the β function of the order parameter from the numerical data, and observe that it may not admit a one-parameter scaling form and a simple Wilson-Fisher fixed point. Rather, it appears to be more compatible with a two-parameter, Berezinskii–Kosterlitz-Thouless-like flow with a line of fixed points (the many-body localized phase) terminating at the localization transition critical point. We argue that this renormalization group framework provides a more coherent and intuitive explanation of numerical data, up to the system sizes available with the present technology.

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Phys. Rev. B 112, 144201– Published 1 October, 2025
  • Received 20 January 2025
  • Revised 15 September 2025
  • Accepted 17 September 2025
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