Many-Body Localization Transition in the Heisenberg Ising Chain

In this paper, we use exact matrix diagonalization to explore the many-body localization (MBL) transition of the Heisenberg Ising spin-1/2 chain with nearest neighbor couplings and disordered external fields. It demonstrates that the fidelity, magnetization and spin-spin space correlation can be used to characterize the many-body localization transition in this closed spin system which is also in agreement with previous analytical and numerical results. We test the properties for the middle third many-body eigenstates. It shows that for this model with random-field, the excited-state fidelity exhibits a pronounced drop at the transition and then gradually tends to be stable in the localized phase, the critical point and the final value of averaged fidelity are all size dependent. It demonstrates that disordered external fields drive the occurrence of the MBL transition. Moreover, we investigate the magnetization and spin-spin space correlation in this model to verify the conclusion we got and further explore the properties of ergodic phase and localized phase.