Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains

TL;DR

This paper investigates spectral correlations and quantum chaos in driven fermionic chains with long-range interactions, showing that spectral form factors align with random matrix theory predictions beyond the Thouless time, which scales with system size.

Contribution

It analytically connects spectral form factors in Floquet fermionic chains to classical spin chain gaps, revealing how long-range interactions influence chaos timescales.

Findings

Spectral form factor matches random matrix theory predictions.

Thouless time scales as L^2 with U(1) symmetry and as L^0 without.

Spectral gap behavior relates to classical spin chain models.

Abstract

We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions, in the presence and absence of particle number conservation ($U(1)$) symmetry. We analytically show that the spectral form factor precisely follows the prediction of random matrix theory in the regime of long chains, and for timescales that exceed the so-called Thouless/Ehrenfest time which scales with the size $L$ as ${\cal O}(L^2)$, or ${\cal O}(L^0)$, in the presence, or absence of $U(1)$ symmetry, respectively. Using random phase assumption which essentially requires long-range nature of interaction, we demonstrate that the Thouless time scaling is equivalent to the behavior of the spectral gap of a classical Markov chain, which is in the continuous-time (Trotter) limit generated, respectively, by a gapless $XXX$, or gapped $XXZ$, spin-1/2 chain Hamiltonian.