Spectral statistics and many-body quantum chaos with conserved charge

Journal article

We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor K(t) analytically for a minimal Floquet circuit model that has a U(1) symmetry encoded via spin-1/2 degrees of freedom. Averaging over an ensemble of realizations, we relate K(t) to a partition function for the spins, given by a Trotterization of the spin-1/2 Heisenberg ferromagnet. Using Bethe ansatz techniques, we extract the “Thouless time” t_Th demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for K(t) at t≲t_Th. We also report numerical results for K(t) in a generic Floquet spin model, which are consistent with these analytic predictions.

Authors: Friedman, A; Chan, A; Luca, A; Chalker, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review Letters
• Volume: 123
• Article number: 210603
• Publication date: 2019-11-22
• Acceptance date: 2019-10-30
• DOI: 10.1103/PhysRevLett.123.210603
• EISSN: 1079-7114
• ISSN: 0031-9007
• Keywords: FFR