Random matrix spectral form factor in kicked interacting fermionic chains

Roy, Dibyendu (author), Prosen, Tomaž (author)

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 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 a random phase assumption which essentially requires a long-range nature of the 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.

• Language: English
• Keywords: statistical physics, nonlinear dynamics, quantum chaos
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2020
• Number of pages: Str. 060202-1-060202-5
• Numbering: Vol. 102, iss. 6
• PID: 20.500.12556/RUL-130383
• UDC: 536.93
• ISSN on article: 2470-0045
• DOI: 10.1103/PhysRevE.102.060202
• COBISS.SI-ID: 76257539
• Publication date in RUL: 14.09.2021

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., E
• Publisher: American Physical Society
• ISSN: 2470-0045
• COBISS.SI-ID: 2048366611

Secondary language

• Language: Slovenian
• Keywords: statistična fizika, nelinearna dinamika, kvantni kaos

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open Many-body Non-Equilibrium Systems
• Acronym: OMNES

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika