Crystalline Spectral Form Factors
Phys. Rev. Lett. 136, 250405 – Published 26 June, 2026
DOI: https://doi.org/10.1103/94cc-zdbl
Abstract
We investigate crystallinelike behavior of the spectral form factor in unitary quantum systems with extremely strong eigenvalue repulsion. Using a low-temperature Coulomb gas as a model of repulsive eigenvalues, we derive the Debye-Waller factor suppressing periodic oscillations of the spectral form factor and estimate the order of its singularities at multiples of the Heisenberg time. We also reproduce this crystallinelike behavior using perturbed permutation circuits and random matrix ensembles associated with Lax matrices. Our results lay a foundation for future studies of quantum systems that exhibit intermediate level statistics between standard random matrix ensembles and permutation circuits.
