  We study a canonical many-body-localized (MBL) system with
power-law-correlated disorders: $s=\frac{1}{2}$ spin chain in a random magnetic
field. The power-law-correlated disorder can control the critical regime
between the MBL and thermal (ergodic) phases by varying its exponent, and it
let us investigate the MBL transitions in detail. Static-eigenstate and dynamic
properties of MBL are studied by numerical methods for systems with various
long-range correlations. By using energy-resolved distribution of the
participation ratio (PR) and calculating some physical quantities related to
localization length, we show that the MBL transition exhibits certain universal
behavior. We also investigate entanglement properties for the static and
dynamics system. These studies elucidate the impact of power-law-correlated
disorders in the canonical MBL system.
