Many-body localization properties of one-dimensional anisotropic spin-1/2 chains

In this paper, we theoretically investigate the many-body localization (MBL) properties of one-dimensional anisotropic spin-1/2 chains by using the exact matrix diagonalization method. Starting from the Ising spin-1/2 chain, we introduce different forms of external fields and spin coupling interactions, and construct three distinct anisotropic spin-1/2 chain models. The influence of these interactions on the MBL phase transition is systematically explored. We first analyze the eigenstate properties by computing the excited-state fidelity. The results show that MBL phase transitions occur in all three models, and that both the anisotropy parameter and the finite system size significantly affect the critical disorder strength of the transition. Moreover, we calculated the bipartite entanglement entropy of the system, and the critical points determined by the intersection of curves for different system sizes are basically consistent with those obtained from the excited-state fidelity. Then, the dynamical characteristics of the systems are studied through the time evolution of diagonal entropy, local magnetization, and fidelity. These observations further confirm the occurrence of the MBL phase transition and allow for a clear distinction between the ergodic (thermal) phase and the many-body localized phase. Finally, to examine the effect of additional interactions on the transition, we incorporate Dzyaloshinskii–Moriya (DM) interactions into the three models. The results demonstrate that the MBL phase transition still occurs in the presence of DM interactions. However, the anisotropy parameter and finite system size significantly affect the critical disorder strength. Moreover, the critical behavior is somewhat suppressed, indicating that DM interactions tend to inhibit the onset of localization.