Chaos and ergodicity in extended quantum systems with noisy driving

Journal article

We study the time evolution operator in a family of local quantum circuits with random elds in a xed direction. We argue that the presence of quantum chaos implies that at large times the time evolution operator becomes eectively 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 generalised spectral form factor  and compare it with the prediction of Random Matrix Theory (RMT). We show that for the systems under consideration the generalised spectral form factor can be expressed in terms of dynamical correlation functions of local observables in the innite temperature state, linking chaotic and ergodic properties of the systems. This also provides a connection between the many-body Thouless time τth  the time at which the generalised spectral form factor starts following the random matrix theory prediction  and the conservation laws of the system. Moreover, we explain dierent scalings of τth with the system size, observed for systems with and without the conservation laws.

Authors: Kos, P; Bertini, B; Prosen, T

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review Letters
• Volume: 126
• Article number: 190601
• Publication date: 2021-05-10
• Acceptance date: 2021-04-07
• DOI: 10.1103/PhysRevLett.126.190601
• EISSN: 1079-7114
• ISSN: 0031-9007
• Language: English
• Keywords: FFR