Many-body localization and enhanced nonergodic subdiffusive regime in the presence of random long-range interactions

We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of random interactions V-ij decaying as power-law V-ij/(r(ij))(alpha) with distance r(ij) We demonstrate that MBL survives even for alpha < 1 and is preceded by a broad nonergodic subdiffusive phase. Starting from parameters at which the short-range interacting system shows an infinite temperature MBL phase, turning on random power-law interactions results in many-body mobility edges in the spectrum with a larger fraction of ergodic delocalized states for smaller values of alpha. Hence, the critical disorder h(c)(r), at which ergodic to nonergodic transition takes place, increases with the range of interactions. Time evolution of the density imbalance I(t), which has power-law decay I(t) similar to t(-gamma) in the intermediate to large time regime, shows that the critical disorder h(c)(I), above which the system becomes diffusionless (with gamma similar to 0) and transits into the MBL phase, is much larger than h(c)(r). In between h(c)(r) and h(c)(I) there is a broad nonergodic subdiffusive phase, which is characterized by the Poissonian statistics for the level spacing ratio, multifractal eigenfunctions, and a nonzero dynamical exponent gamma << 1/2. The system continues to be subdiffusive even on the ergodic side (h < h(c)(r)) of the MBL transition, where the eigenstates near the mobility edges are multifractal. For h < h(0) < h(c)(r), the system is superdiffusive with gamma > 1/2. The rich phase diagram obtained here is unique to the random nature of long-range interactions. We explain this in terms of the enhanced correlations among local energies of the effective Anderson model induced by random power-law interactions.

Automated summary

In a one-dimensional system of spinless fermions, many-body localization (MBL) is studied in the presence of random interactions decaying as a power-law. The system exhibits a broad nonergodic subdiffusive phase before MBL, and the critical disorder for the ergodic to nonergodic transition increases with the range of interactions. Random power-law interactions induce multifractal eigenfunctions and nonergodic subdiffusive phase in the spectrum of the system.