Quench dynamics in the one-dimensional mass-imbalanced ionic Hubbard model

Abstract

Using the time-dependent Lanczos method, we study the nonequilibrium dynamics of the one-dimensional ionic-mass imbalanced Hubbard chain driven by a quantum quench of the on-site Coulomb interaction, where the system is prepared in the ground state of the Hamiltonian with a different Hubbard interaction. The exact diagonalization method (Lanczos algorithm) is adopted to study the zero temperature phase diagram in equilibrium, which is shown to be in good agreement with previous studies using density matrix renormalization group (DMRG). We then study the nonequilibrium quench dynamics of the spin and charge order parameters by fixing the initial and final Coulomb interactions while changing the quenching time protocols. Our study shows that the time evolution of the charge and spin order parameters strongly depend on the quenching time protocols. In particular, the effective temperature of the system will decrease monotonically as the quenching time is increased. By taking the final Coulomb interaction strength to be in the strong coupling regime, we find that the oscillation frequency of the charge order parameter increases monotonically with the Coulomb interaction. By contrast, the frequency of the spin order parameter decreases monotonically with increasing Coulomb interaction. We explain this result using an effective spin model and a two-site Hubbard model in the strong coupling limit. Finally, we take the final Coulomb interaction strength to be in the weak coupling regime and find that the oscillation frequency of both the charge and spin order parameters increases monotonically with decreasing Coulomb interaction. Our study suggests strategies to engineer the relaxation behavior of interacting quantum many-particle systems.