Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains

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 $\mathcal{O}(L^2)$, or $\mathcal{O}(L^0)$, 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.

6 pages, 1 figure

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• Semiclassical Foundation of Universality in Quantum Chaos
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Non-universal level statistics in a chaotic quantum spin chain

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