Spectral statistics of driven Bose-Hubbard models

We study the spectral statistics of a one-dimensional Bose-Hubbard model subjected to kinetic driving; a form of Floquet engineering where the kinetic energy is periodically driven in time with a zero time-average. As the amplitude of the driving is increased, the ground state of the resulting flat-band system passes from the Mott insulator regime to an exotic superfluid. We show that this transition is accompanied by a change in the system's spectral statistics from Poisson to GOE-type. Remarkably, and unlike in the conventional Bose-Hubbard model which we use as a benchmark, the details of the GOE statistics are sensitive to the parity of both the particle number and the lattice sites. We show how this effect arises from a hidden symmetry of the Hamiltonian produced by this form of Floquet driving.