The Behavior Of Many-body Localization In The Periodically Driven Heisenberg XXX Model

In this paper,we use exact matrix diagonalization to research properties of the many-body localization(MBL)in the Heisenberg XXX spin 1/2 chain model with periodic driving.We establish the period-driven system by adding a time-periodic field consisting of trigonometric function to the closed and disordered Heisenberg XXX model.It is demonstrated that the fidelity of eigenstate is able to capture quantum criticality underlying many-body physics,which can be used to characterize the many-body localization transition in this closed spin system.We obtain the fidelity for high-energy many-body eigenstates,namely,the excited state fidelity,which shows the phase transition of periodically driven Heisenberg XXX spin 1/2 chain with different disordered external field strengths and different system sizes.It is shown that when the system is in a very small disorder,periodic driving can cause occurrence of a transition from ergodic phase to MBL phase of the disordered system.For a many-body disordered system in a localized phase,there will exist a critical driven period T,when driven period T is higher than T,the system will undergo a transition from localized phase to ergodic phase and MBL phase will be broken.Conversely,the system will remain in MBL phase when the driven period T is under the critical value T.Furthermore,we discover that the size of the system and the strength of disorder will affect the critical point of driven period and the magnitude of the phase change.For the same system,the critical point increases as the strength of disorder increases.That is,the larger the disorder,the more stable the localized phase and the higher the critical driven period required for the phase transition to occur.To further study the property of MBL phase,we have comparatively investigated the phase transition under the Haldane-Shastry(H-S)model which considers long-range interactions.The results show that the period-driven Heisenberg XXX model and the H-S model obtain different results in the same conditions.When the drive is in the H-S system of the ergodic phase,no many-body localized phase transition occurs,which illustrates the important influence of interactions in the many-body localization properties.In addition we have studied the corresponding non-disordered system at h = 0.5 under the same periodic driving and the results show that the system undergoes ground state quantum-phase transition rather than many-body localized phase transition.This suggests that disorder plays an important role in the properties of the many-body localization.