# Publications associated with Condensed Matter Theory

## Spectral statistics and many-body quantum chaos with conserved charge

Phys. Rev. Lett. 123 (2019) 210603-210603

AJ Friedman, A Chan, AD Luca, JT Chalker

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.

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