Quench Dynamics In The One-dimensional Mass-imbalanced Ionic Hubbard Model

In the field of condensed matter physics,the investigation of strongly correlated electronic systems has always been a prominent topic due to its complex nature.Recent advances have been made in both theoretical and experimental research on the nonequilibrium dynamics of these systems.However,the dynamic behavior of various physical quantities in strongly correlated electronic systems during non-equilibrium evolution is not determined by a single degree of freedom,but instead,is influenced by the entanglement of different degrees of freedom within the system.In this paper,we mainly study the nonequilibrium dynamics of the one-dimensional mass-imbalanced ionic Hubbard model.In addition to discussing the physical properties of the model in various equilibrium states,we also analyze the quenching dynamics of the system from the perspective of different energy gaps.Our study can be tested experimentally in cold atomic optical lattices,and the findings can provide useful insights into the relaxation behavior of interacting quantum multiparticle systems.In Chapter One,we provide a comprehensive introduction to the one-dimensional Hubbard model and its fundamental physical significance.This model is a simple yet effective way to describe correlation effects in one-dimensional electronic systems,and various extended Hubbard models have been developed to meet specific experimental requirements.Due to the collective impact of correlation effects within the system,distinct phases emerge under varying conditions.We employ Landau’s phase transition theory to characterize the phase transition behavior,and then elaborate on the importance of studying the non-equilibrium dynamics of strongly correlated electronic systems.In Chapter Two,we utilize the one-dimensional Hubbard model as a case study to present a detailed explanation of the exact diagonalization algorithm’s calculation process in the equilibrium state.We also briefly discuss the generalization and application of this method in non-equilibrium states and finite temperatures.In Chapter three,we first start from the equilibrium system corresponding to the one-dimensional mass-imbalanced ionic Hubbard model,and analytically deal with the effective Hamiltonian of the system at the non-interacting limit and the strong interacting limit by using the Bogoryubov change and the effective Hamiltonian approximation,so as to obtain the physical properties under the two limits.In addition,we also discuss the phase transition of the system with respect to the coulomb interaction by combining the block entropy and different energy gaps.Finally,the zero temperature phase transition point and zero temperature phase diagram of the coulomb interaction are calculated by the exact diagonalization method.The results show that the exact diagonalization is in good agreement with the results of the density matrix renormalization group.In Chapter Four,we investigate the non-equilibrium dynamics of the system after a quantum quench of the Coulomb interaction using a time-dependent diagonalization method.We extend the order parameters of the system to time-dependent expressions and analyze their evolution behavior from three perspectives: quenching time,strong and weak interaction at the final state.We provide a reasonable physical explanation for the observed behaviors.Our study of the non-equilibrium evolution of spin and charge sequence parameters reveals that their behavior is highly dependent on the quenching time.We find that the effective temperature of the system decreases monotonically with the increase of quenching time,and the mean values of the charge and spin order parameters are close to their respective equilibrium values at the corresponding effective temperature.We then set the final Coulomb interaction strength to the strong interaction limit and observe that the dynamics of the two order parameters are different.The frequency of the charge density order parameter increases monotonically with the Coulomb interaction,while the frequency of the spin density order parameter decreases monotonically with the Coulomb interaction.To explain this result theoretically,we use the XXZ model and the two-lattice Hubbard model under the strong interaction limit.Finally,we consider the case where the final Coulomb interaction strength is weak,and observe that the oscillation frequencies of the charge and spin density order parameters increase monotonically with the decrease of Coulomb interaction.This behavior is due to the charge energy gap and excitation gap of the Hamiltonian in the equilibrium state.