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  • Open Access

Identifying mobility edge from finite temperature spectral form factor

Basudha Roy*

Adway Kumar Das‡

Anandamohan Ghosh†

  • *Contact author: br23rs008@iiserkol.ac.in
  • †Contact author: anandamohan@iiserkol.ac.in
  • ‡Contact author: a.k.das@lboro.ac.uk
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Phys. Rev. B 114, 034203 – Published 6 July, 2026

DOI: https://doi.org/10.1103/szn3-qp7d

Abstract

The spectral form factor (SFF) is a measure of energy correlations and has been widely used to identify the transition from the ergodic to the localized phase in interacting many-body quantum systems. In this work, we show that in a disordered Heisenberg spin-12 model, the finite temperature SFF can be used to generate a canonical phase diagram exhibiting a critical temperature TMBL. Using simple ideas of statistical mechanics, we obtain the critical energy density εMBL dual to TMBL. We show that the mobility edge, numerically estimated from the spread of local perturbations and the optical conductivity, indeed coincides with εMBL.

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Phys. Rev. B 114, 034203– Published 6 July, 2026
  • Received 29 January 2026
  • Revised 21 May 2026
  • Accepted 12 June 2026
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