Thermalization after an ionic potential quench in the Ionic Hubbard Mode

Here we study the consequences of an ionic potential quench in the Ionic Hubbard Model on a Bethe lattice using non-equilibrium Dynamical Mean Field Theory. The system is quenched from a staggered charge density order(ionic potential Δ≠0) to a uniform state(for Δ = 0) for different values of the interaction U. We find that the staggered occupancy(δn) decreases rather fast from its initial value(for Δ ≠0) to the final δn =0(which is equilibrium δn when Δ = 0) , but in an oscillatory fashion. At large times(t > 3.0 $\hbar$/J, where J is the nearest neighbor hopping amplitude) these oscillations can be well fitted by a function of the form [Acos(ωt+φ)\exp{-Γ t}]/t^α. As one increases U the frequency of the oscillation(ω) is almost constant(≈4*J/$\hbar$) but the rate of decay of the oscillations, Γ, increases with increasing U, where as α deceases. When U =0 α ≈ 1.5 and Γ ≈ 0.0. We also find that none of the three fitting parameters (ω,α,Γ) depend on the initial staggered potential. It remains a challenging question to understand the microscopic origins of these parameters. We have also studied the evolution of the double occupancy under these quenches, and while it also thermalizes, its time dependence seems more complicated.