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

We study spectral form factor in periodically kicked bosonic chains. We consider a family of models where a Hamiltonian with the terms diagonal in the Fock space basis, including random chemical potentials and pairwise interactions, is kicked periodically by another Hamiltonian with nearest-neighbor hopping and pairing terms. We show that, for intermediate-range interactions, the random phase approximation can be used to rewrite the spectral form factor in terms of a bistochastic 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 pairing terms. In such a case, we numerically find a nontrivial systematic system-size dependence of the Thouless time, in contrast to a related recent study for kicked fermionic chains.

Automated summary

In this study, we investigate the spectral form factor in periodically kicked bosonic chains. By using the random phase approximation, we demonstrate that the spectral form factor can be rewritten in terms of a bistochastic many-body process generated by an effective bosonic Hamiltonian. This research provides important insights into the system size effects and the relationship between particle number and spectral properties.