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arXiv · 2606.15294

Identifying mobility edge from finite temperature spectral form factor

Basudha Roy·Anandamohan Ghosh·Adway Kumar Das
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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-$\frac{1}{2}$ model, the finite temperature SFF can be used to generate a canonical phase diagram exhibiting a critical temperature $T_\mathrm{MBL}$. Using simple ideas of statistical mechanics, we obtain the critical energy density $\epsilon_\mathrm{MBL}$ dual to $T_\mathrm{MBL}$. We show that the mobility edge, numerically estimated from the spread of local perturbations and the optical conductivity, indeed coincides with $\epsilon_\mathrm{MBL}$.

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Basudha Roy, Anandamohan Ghosh, Adway Kumar Das. 2026-06-13. Identifying mobility edge from finite temperature spectral form factor. https://doi.org/10.1103/szn3-qp7d

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