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Signatures of nonergodicity in sparse random matrices

Sagnik Seth1,*, Adway Kumar Das2,†, and Anandamohan Ghosh1,‡

  • *Contact author: ss22ms026@iiserkol.ac.in
  • †Contact author: A.K.Das@lboro.ac.uk
  • ‡Contact author: anandamohan@iiserkol.ac.in
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Phys. Rev. B 114, 144204 – Published 16 September, 2026

DOI: https://doi.org/10.1103/x4tm-9249

Abstract

The prevalence of sparsity in the Fock space graph of interacting many-body systems motivates an investigation into the spectral statistics of sparse random matrices with on-site disorder. We numerically determine the delocalization-localization transition in the ground state as a function of the sparsity. The short-range energy correlation in the bulk indicates that the Anderson transition at infinite temperature occurs at the critical percolation limit of the sparse graph. By analytically deriving the energy moments and calculating the shifted kurtosis, we show that the critical sparsity threshold matches the Anderson transition. Furthermore, long-range energy correlations in the bulk spectrum reveal a Thouless energy scale, suggesting a broad nonergodic regime within the delocalized phase.

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Phys. Rev. B 114, 144204– Published 16 September, 2026
  • Received 3 April 2026
  • Revised 14 August 2026
  • Accepted 20 August 2026
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