Many-Body Localization Properties Of The Onedimensional Heisenberg Model With Quasi-Periodic Potential

Many-body localization is an extended form of Anderson localization that considers interactions between particles,it can prevent the thermalization of the system,protect the quantum order,and facilitate the storage and calculation of quantum information.Therefore,many-body localization is a hot topic in the research of quantum information.The present research shows that we can make the many-body localization phase transition by placing the system in a disordered field,a quasi-periodic potential field,or applying periodic driving to the system.In this thesis,we mainly study the many-body localization properties of the one-dimensional Heisenberg model with quasi-periodic potential,and the effect of periodic driving on its properties.We use trigonometric functions to construct four different forms of quasi-periodic potential,then select a certain number of eigenstates and quasi-periodic potential realization,and average them to calculate the averaged excited state fidelity E[F]and local magnetization of the system,and plot the variation curve of E[F]with the quasi-periodic potential strength h.By observing the variation of the curve,we find that the one-dimensional Heisenberg model with quasi-periodic potential can occur the many-body localization phase transition.In addition,we also use the local magnetization to further verify the occurrence of manybody localization phase transition in the quasi-periodic system.The results show that when the quasi-periodic potential strength h is small,the system is in the ergodic phase;and when the quasi-periodic potential strength h is large,the system is in the localized phase.And the form of quasi-periodic potential,the system size N all effect the critical quasi-periodic potential strength hc of the many-body localization phase transition.The critical quasi-periodic potential strength hc of phase transition can be controlled by selecting different forms of quasi-periodic potential field,this further indicates that the quasi-periodic potential field has certain advantage compared with the uncontrollability of the critical disorder strength hc in the disordered field,and is conducive to more comprehensive research.In addition,we find that as the system size N increases,the critical quasi-periodic potential strength hc of the one-dimensional Heisenberg model with quasi-periodic potential decreases.This indicates that the interaction between particles also has some influence on the many-body localization properties of Heisenberg model.On this basis,we apply the time-periodic field in the form of trigonometric function to the one-dimensional Heisenberg model with periodic potential,and further study the many-body localization properties of the periodic driving one-dimensional Heisenberg model with quasi-periodic potential.By adjusting the quasi-periodic strength h,we let the quasi-periodic potential system with periodic driving initially be in the ergodic phase and localized phase respectively.Then we discuss whether the periodic driving can make the quasi-periodic potential system occur the many-body localization or delocalization phase transition respectively.It is found that the periodic driving can make the system occur these two phase transitions,and the critical driving period Tc is not only related to the quasi-periodic potential strength h,but also to the system size N.We compare the curves of different quasi-periodic potential strength h and find that when the periodically driven system is initially in the ergodic phase(h<hc),the critical driving period Tc decreases as the quasi-periodic potential strength h increases;and when the system is initially in the localized phase(h>hc),Tc increases as the quasi-periodic potential strength h increases.For the system size N,no matter the periodically driven system is initially in the ergodic phase or localized phase,Tc all decreases as the system size N increases.