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We study a canonical many-body-localized (MBL) system withpower-law-correlated disorders: $s=\frac{1}{2}$ spin chain in a random magneticfield. The power-law-correlated disorder can control the critical regimebetween the MBL and thermal (ergodic) phases by varying its exponent, and itlet us investigate the MBL transitions in detail. Static-eigenstate and dynamicproperties of MBL are studied by numerical methods for systems with variouslong-range correlations. By using energy-resolved distribution of theparticipation ratio (PR) and calculating some physical quantities related tolocalization length, we show that the MBL transition exhibits certain universalbehavior. We also investigate entanglement properties for the static anddynamics system. These studies elucidate the impact of power-law-correlateddisorders in the canonical MBL system.

Effects of power-law correlated disorders in XXZ spin chain: Many-body localized to thermal phase transition and its critical regime