Solution of a minimal model for many-body quantum chaos

TL;DR

This paper introduces an exactly solvable minimal model for many-body quantum chaos in a spatially extended system, analyzing spectral, entanglement, and operator dynamics using diagrammatic methods.

Contribution

It presents a novel solvable model of quantum chaos with a specific Floquet circuit structure, providing exact large-q results for key dynamical quantities.

Findings

Exact expressions for spectral form factor

Results on local observable relaxation

Analysis of entanglement growth and operator spreading

Abstract

We solve a minimal model for quantum chaos in a spatially extended many-body system. It consists of a chain of sites with nearest-neighbour coupling under Floquet time evolution. Quantum states at each site span a $q$-dimensional Hilbert space and time evolution for a pair of sites is generated by a $q^2\times q^2$ random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbour on one side during the first half of the evolution period, and to its neighbour on the other side during the second half of the period. We show how dynamical behaviour averaged over realisations of the random matrices can be evaluated using diagrammatic techniques, and how this approach leads to exact expressions in the large-$q$ limit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth and operator spreading.