Properties of many-body localization in quasi-disordered Haldane–Shastry model

In this work, through the exact matrix diagonalization, we theoretically study the properties of many-body localization (MBL) in one-dimensional quasi-disordered Haldane–Shastry chains. The Haldane–Shastry (HS) model is an integrable quantum spin chain with long-range interactions, it is the generalized Heisenberg XXX model which only contains the nearest-neighbor two-body interactions. By studying the HS model, it is worth noting that we extend the MBL problem of disordered systems to quasi-disordered many-body systems, where the quasi-disorder is adjustable. Firstly, we use excited-state fidelity to study the phase transition, it is found that the interplay between quasi-disorder and interaction can cause the system to occur the many-body localized phase transition, which is similar to that in the random disordered systems. It shows that quasi-disorder forms and system size both affect the critical point of the MBL phase transition. Secondly, we use local magnetization to further demonstrate that the many-body localized phase transition does occur in the quasi-disordered HS model. We also discuss the effect of periodic driving on the quasi-disordered HS systems. It shows that periodic driving will cause the quasi-disordered systems to occur the phase transition between the ergodic phase and the localized phase.