Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains

• URL: http://arxiv.org/abs/2005.10489v1
• Date: Thu, 21 May 2020 07:02:04 GMT
• Title: Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains
• Authors: Dibyendu Roy and Toma\v{z} Prosen
• Abstract summary: We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions. We analytically show that the spectral form factor precisely follows the prediction of random matrix theory in the regime of long chains.
• Score: 1.6295305195753724
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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