The Behavior of Many-Body Localization of Quasi-Disordered Spin-1/2 Chains

We theoretically study properties of the many-body localization (MBL) in the quasi-disordered one-dimensional spin-1/2 chains at finite temperature. We extend the problem of individual localization of disordered systems to quasi-disordered many-body interaction systems, introducing disorder with a more controllable method to show the uniqueness of quasi-disordered designs. In this paper, the interplay among interaction and quasi-disordered fields is investigated comprehensively by using the exact matrix diagonalization. It is demonstrated that the fidelity of eigenstate is able to characterize the many-body localization transition in closed spin system (Gu, Int. J. Mod. Phys. B 24 , 4371–4458, 2010 ). We compute the fidelity for high-energy many-body eigenstates, which shows the phase transition of one-dimensional spin-1/2 chains. Our results reveal that the quasi-disordered can cause the occurrence of a transition from the ergodic phase to the localized phase, which agrees with Lee’s recent studies (Lee et al., Phys. Rev. B 96 , 075146, 2017 ). Besides, we plot the averaged fidelity as a function of the disorder strength h for system sizes from 8 to 14 with five different coupling coefficient ratios. It also shows that the interplay between disorder and interaction constitutes the driving mechanism of the MBL transition. The more complex the interaction between the two particles, the more difficult it is to lead to many-body delocalization.