Spectral form factor in a minimal bosonic model of many-body quantum chaos

Dibyendu Roy, Divij Mishra, Tomaž Prosen

Published 2022-03-10Version 1

We study spectral statistics and especially the spectral form factor in Floquet driven (kicked) bosonic chains. We consider a family of models where free boson Hamiltonian with the nearest neighbor hopping and possibly pairing terms is kicked with the terms diagonal in the Fock space basis, including random chemical potentials and pair-wise interactions. It is shown that for intermediate-range interactions, random phase approximation can be used to rewrite the spectral form factor in terms of a bi-stochastic many-body process generated by an effective bosonic Hamiltonian. In the particle-number conserving case, i.e., when pairing terms are absent, the effective Hamiltonian has a non-abelian $SU(1,1)$ symmetry, resulting in universal quadratic scaling of the Thouless time with the system size, irrespective of the particle number. This is a consequence of degenerate symmetry multiplets of the subleading eigenvalue of the effective Hamiltonian and is broken by the particle number breaking pairing terms. In the latter case, we numerically find a nontrivial systematic dependence of the Thouless time on the system size, in contrast to a related recent study for kicked fermionic chains.