Property of Many-Body Localization in Heisenberg Ising Chain Under Periodic Driving

We study the property of the many-body localization in Heisenberg Ising Chain model with periodic driving by using the method of matrix exact diagonalization. We consider a driving protocol in which the system’s Hamiltonian is periodically switched between two operators. The first segment is a disordered Ising system, and acts for time T 0 ; It is worth noting that the Hamiltonian of the second part is an operator dependent on time, and acts for time T 1 , so the driving period is T = T 0 + T 1 . We choose excited state fidelity to observe the phase transition between the localized phase and the ergodic phase of the system, which reflects the property of many-body localization in Heisenberg Ising Chains under periodic driving. Through the study, we find that when the disorder strength h is small, the system is in the ergodic phase, periodic driving can cause the occurrence of a transition from the ergodic phase to the localized phase, while the system is in the localized phase with a large disorder strength h , the transition from the localized phase to the ergodic phase will occur under the periodic driving. For these two cases, they all show that there is a critical driving period T c , when the driving period is greater than T c , the system will have a phase transition, meanwhile, T c decreases with the increase of driving strength. Furthermore, we also get that the system size and disorder strength also effect the critical point of the driving period. The critical point decreases as the strength of disorder increases and decreases with the increase of the system size.