Spectral statistics and many-body quantum chaos with conserved charge
Phys. Rev. Lett. 123 (2019) 210603-210603
Authors:
Aaron J Friedman, Amos Chan, Andrea De Luca, JT Chalker
Abstract:
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.
