Nonequilibrium Charge Correlation Effects In One-Dimensional Superlattices

Strong correlated electron systems have long been a hot topic in condensed matter physics.Many materials,including high temperature superconductors and heavy fermion materials,need to be described by strong correlation models.Hubbard model as one of the most basic models has been widely used.It can be used to describe many strongly correlated materials and to analyse them theoretically.As real materials often contain different types of atoms,it is necessary to consider heterogeneity from a model perspective.In recent years,with the development of optical technology,the dynamic properties of laser-induced materials have attracted wide attention,and many exotic quantum phenomena that cannot be observed in equilibrium state have been discovered.Therefore,in this paper,from the perspective of theoretical calculation,the exact diagonalization method is used to study the one-dimensional superlattice(A-B sublattice)Hubbard model,and focuses on the nonequilibrium dynamical behaviour of the model.In Chapter 3,the two-site superlattice model is studied under different ensembles.In the equilibrium state,the results show that with the increase of temperature,the average double occupancy of the system at site A and site B will be inconsistent under the grand canonical ensemble,and the total energy of the system under the grand canonical ensemble is higher than that of the canonical ensemble.The study of model non-equilibrium focuses on the system under the great canonical ensemble.The externally modulated spectrum is considered,and couple it into the kinetic energy of the model Hamiltonian,driving the system into a non-equilibrium state.It is found that under the action of this external field,the system energy and average double occupancy show oscillatory behavior with time,and with the increase of temperature,the amplitude of the oscillation becomes smaller and smaller,but the oscillation period is basically the same,which is related to the period of the modulation spectrum(2π/ω).This shows that the oscillatory behavior of the system energy and average double occupancy is dominated by the period of the applied spectrum.In Chapter 4,The non-equilibrium dynamic evolution behavior of the one-dimensional superlattice Hubbard model(A-B sublattice)after being subjected to an applied laser is studied.In equilibrium,the critical points of the charge correlation commensurabilityincommensurability are studied in the parameter plane of Coulomb interaction and on-site potential energy.The results show that the exact diagonalization method is in good agreement with those obtained by density matrix renormalization group.Non-equilibrium studies are focused on the particle-hole symmetric points.The initial state is the ground state of the equilibrium Hamiltonian at starting time.The non-equilibrium evolution of physical observables,such as the total energy,double occupation and charge correlation function,are investigated while an external laser is applied.Numerical studies show that for a system with commensurate charge correlation,the transition from commensurate to incommensurate charge correlation will occur depending on the parameters of laser.By analyzing the time-dependent data of the charge correlation function,it is found that the charge correlation between the even sites in the system is enhanced under the action of the laser,which eventually leads to the incommensurate charge correlation.The results provide strategies for ultrafast control of the charge ordering in superlattice.