We address the critical properties of the many-body localization (MBL) phase transition in one-dimensional systems subject to spatially correlated disorder. Rather than starting from a microscopic model, we analyze the transition within a strong-randomness renormalization group (RG) framework. We introduce disorder directly at the level of scaling variables appearing in the RG and consider a general family of spatial correlations, parameterized by how strong the fluctuations of the disordered couplings are when coarse-grained over a region of size $\ensuremath{\ell}$. For uncorrelated randomness, the characteristic scale for these fluctuations is $\sqrt{\ensuremath{\ell}}$; more generally they scale as ${\ensuremath{\ell}}^{\ensuremath{\gamma}}$. We discuss both positively correlated disorder ($1/2<\ensuremath{\gamma}<1$) and anticorrelated, or ``hyperuniform,'' disorder ($\ensuremath{\gamma}<1/2$). We argue that anticorrelations in the disorder are generally irrelevant at the MBL transition. Moreover, assuming the MBL transition is described by the recently developed renormalization-group scheme of Morningstar et al. [Phys. Rev. B 102, 125134 (2020)], we argue that even positively correlated disorder leaves the critical theory unchanged, although it modifies certain properties of the many-body localized phase.
The disordered many-body systems can undergo a transition from the extended ensemble to a localized ensemble, known as many-body localization (MBL), which has been intensively explored in recent years. Nevertheless, the relation between Anderson localization (AL) and MBL is still elusive. Here we show that the MBL can be regarded as an infinite-dimensional AL with the correlated disorder in a virtual lattice. We demonstrate this idea using the disordered XXZ model, in which the excitation of
d spins over the fully polarized phase can be regarded as a single-particle model in a
d dimensional virtual lattice. With the increasing of
d, the system will quickly approach the MBL phase, in which the infinite-range correlated disorder ensures the saturation of the critical disorder strength in the thermodynamic limit. From the transition from AL to MBL, the entanglement entropy and the critical exponent from energy level statics are shown to depend weakly on the dimension, indicating that belonging to the same universal class. This work clarifies the fundamental concept of MBL and presents a new picture for understanding the MBL phase in terms of AL.
We study a canonical many-body-localized (MBL) system with power-law-correlated disorders:
s=21 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.