Kos Pavel, Bertini Bruno, Prosen Tomaž
Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia.
Rudolf Peierls Centre for Theoretical Physics, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom.
Phys Rev Lett. 2021 May 14;126(19):190601. doi: 10.1103/PhysRevLett.126.190601.
We study the time-evolution operator in a family of local quantum circuits with random fields in a fixed direction. We argue that the presence of quantum chaos implies that at large times the time-evolution operator becomes effectively a random matrix in the many-body Hilbert space. To quantify this phenomenon, we compute analytically the squared magnitude of the trace of the evolution operator-the generalized spectral form factor-and compare it with the prediction of random matrix theory. We show that for the systems under consideration, the generalized spectral form factor can be expressed in terms of dynamical correlation functions of local observables in the infinite temperature state, linking chaotic and ergodic properties of the systems. This also provides a connection between the many-body Thouless time τ_{th}-the time at which the generalized spectral form factor starts following the random matrix theory prediction-and the conservation laws of the system. Moreover, we explain different scalings of τ_{th} with the system size observed for systems with and without the conservation laws.
