Study On Multi-body Localization Of Extended Mosaic Model

Multi-body localization(MBL)is a very important concept in condensed matter physics.The quantum system in MBL phase does not achieve thermal equilibrium spontaneously,and can retain the initial state information of the quantum system well.Such unique properties and potential applications have aroused great interest among physicists,and understanding the generation mechanism,phase transition behavior and its critical properties has become a hot topic.Research on multi-body localization is also highly feasible experimentally.Atoms placed into the optical lattice on the platform of ultra-cold atoms can simulate a variety of crystal structures.Different experimental schemes can be implemented according to different generation mechanisms,so as to observe different localization behaviors of the system.We first introduce the basic physical concepts in the localization phenomenon,such as the realization of optical lattice,the difference between disorder and quasi-periodic potential,the theory of quasi-periodic lattice,and the concept of mobility edge.Then we introduce the quantum models with localization phenomenon in single particle system: AA model,Mosaic model and Stark model,and describe the Hamiltonian of each models and relevant experimental implementation.The behaviors of the localization of multi-body system is the main research interests of this paper when the correlation between particles exits.Therefore,for multi-body systems,we focus on the localization properties of AA model and Stark model under the interaction,as well as the relevant theory and experimental implementation of multi-body critical phase.Next we investigate the localization of the Mosaic model in the incommensurate optical lattice in the one-dimensional spin-free Fermi system with near-neighbor interaction,and determine the transition point from thermalization to multi-body localization by adjusting the intensity of the interaction and the quasi-periodic potential.The gauge participation rates of the eigenstates corresponding to the ground state and the intermediate one-sixth energy level in the system are calculated by using the accurate diagonalization method.It is found that there is a mixed phase between the thermalized phase and the manybody local phase.In this region,the excited state corresponding to the intermediate level of the system is localized earlier than the ground state,which is different from the mixed phase property of the interaction Aubry-André model.By using the density matrix renormalization group and the exact diagonalization method,the single-particle excitation of density wave function of the ground-state,the ratio of the nearest neighbor energy levels and the entanglement entropy of the excited state are calculated,and the two phase boundaries of the mixed phase are obtained.The numerical results show that the weak quasi-periodic potential can only localize the excited state,but not the ground state in the multi-body system.Finally,we study the correspondence between the localization caused by disorder and Stark localization caused by linear field(or the influence of disorder and disorder-free on localization)in the mosaic lattice.We obtain the ground state entanglement entropy by the accurate diagonalization method,and discuss the contribution of the two intensities to the multi-body localization of the system.It is found that when the two localization mechanisms exist separately,disorder-free has a stronger impact on the system localization.When the same two localization mechanisms exist simultaneously,there is a corresponding relationship between linear potential strength and quasi-periodic potential strength on multi-body local area disorder-free has a greater.