Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains

Dibyendu Roy; Tomaž Prosen

doi:10.1103/PhysRevE.102.060202

paper

Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains

arXiv:2005.10489 · doi:10.1103/PhysRevE.102.060202

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 $O (L^{2})$ , or $O (L^{0})$ , 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 $X X X$ , or gapped $X X Z$ , spin-1/2 chain Hamiltonian.

arXiv comment6 pages, 1 figure

Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains

Abstract

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