Liouvillian gap and single spin-flip dynamics in the dissipative Fermi-Hubbard model

Motivated by recent progress in cold-atom experiments, we analyze the SU(N) Fermi-Hubbard model on a d-dimensional hypercubic lattice with two-body loss. By focusing on states near the ferromagnetic steady states, we obtain the Liouvillian gap in closed form for any d and N. We also investigate the dynamics of a ferromagnetic initial state with a single spin flip analytically in strongly- and weakly-interacting and dissipative limits and numerically for various values of the parameters. Then we show that, by decreasing the strength of the interaction and loss, a crossover from the power-law decay to the exponential decay occurs. We expect that our findings can be tested experimentally with ultracold alkaline-earth-like atoms in an optical lattice.