Physics

Quantum dynamics

Nonlinear system

Charge (physics)

Mathematics

Random matrix

Statistical physics

Statistics

Ansatz

Quantum chaos

Artificial intelligence

Eigenvalues and eigenvectors

Chaotic

Geometry

Partition function (quantum field theory)

Computer science

Spin (aerodynamics)

Floquet theory

Quantum mechanics

Bethe ansatz

Conserved quantity

Quantum

Thermodynamics

Scaling

Physical Review Letters

We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor $K(t)$ analytically for a minimal Floquet circuit model that has a $U(1)$ symmetry encoded via auxiliary spin-$1/2$ degrees of freedom. Averaging over an ensemble of realizations, we relate $K(t)$ to a partition function for the spins, given by a Trotterization of the spin-$1/2$ Heisenberg ferromagnet. Using Bethe Ansatz techniques, we extract the 'Thouless time' $t^{\vphantom{*}}_{\rm Th}$ demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for $K(t)$ at $t\lesssim t^{\vphantom{*}}_{\rm Th}$. We also report numerical results for $K(t)$ in a generic Floquet spin model, which are consistent with these analytic predictions.

Spectral Statistics and Many-Body Quantum Chaos with Conserved Charge