Many-body Localization Transition In The Ising Chain

For the ubiquitous nature of disorder,it is important to understand how disorder behaves in all kinds of systems.This paradigm was brought to the forefront by the seminal work of P.W.Anderson as localization.After the time of Anderson's paper,the localization transition has been discussed by a few authors and became a series of theories: the non-interacting systems in one or two dimensions will be localized for arbitrary disorder,even for very small disorder,which is named Anderson localization.In addition,a closed interacting quantum system with sufficiently strong disorder would fail to approach thermal equilibrium but localize,which is called many-body localization.The system will change from ergodic phase to localized phase with increased disorder.Here we consider combining the previous work to look at this transition more profoundly.In this paper,we use exact matrix diagonalization to explore the many-body localization(MBL)transition of the Heisenberg Ising spin1/2chain 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.