Many-body quantum chaos and space-time translational invariance.

ABSTRACT: We study the consequences of having translational invariance in space and time in many-body quantum chaotic systems. We consider ensembles of random quantum circuits as minimal models of translational invariant many-body quantum chaotic systems. We evaluate the spectral form factor as a sum over many-body Feynman diagrams in the limit of large local Hilbert space dimension q. At sufficiently large t, diagrams corresponding to rigid translations dominate, reproducing the random matrix theory (RMT) behaviour. At finite t, we show that translational invariance introduces additional mechanisms via two novel Feynman diagrams which delay the emergence of RMT. Our analytics suggests the existence of exact scaling forms which describe the approach to RMT behavior in the scaling limit where both t

SUBMITTER: Chan A 

PROVIDER: S-EPMC9722696 | biostudies-literature | 2022 Dec

REPOSITORIES: biostudies-literature