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

TL;DR

This paper investigates the spectral form factor in a minimal bosonic model of many-body quantum chaos, revealing universal scaling behaviors and the effects of pairing terms on system-size dependence.

Contribution

It introduces a bosonic model with periodic kicks, analyzes the spectral form factor using a random phase approximation, and uncovers symmetry-driven universal scaling of the Thouless time.

Findings

Universal quadratic scaling of Thouless time with system size in particle-number conserving case.

Symmetry multiplets cause degeneracies affecting spectral properties.

Pairing terms break symmetry and alter system-size dependence of Thouless time.

Abstract

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 pair-wise interactions, is kicked periodically by another Hamiltonian with nearest-neighbor hopping and pairing terms. We show 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 pairing terms. In the latter 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.