Time evolution

Discrete mathematics

Quantum entanglement

Physics

Graph

Quantum dynamics

Nonlinear system

Operator (biology)

Mathematics

Transcription factor

Gene

Statistical physics

Engineering

Quantum state

Coupling (piping)

Quantum chaos

Unitary operator

Repressor

Bipartite graph

Chemistry

Quantum system

Classical limit

Floquet theory

Quantum mechanics

Observable

Biochemistry

Hilbert space

Mechanical engineering

Quantum

Physical Review X

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.

Solution of a Minimal Model for Many-Body Quantum Chaos