Many-body localization and enhanced non-ergodic sub-diffusive 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 long-range interactions decaying as power-law V_ij/\(r_i-r_j\)^α with distance and having random coefficients V_ij. We demonstrate that MBL survives even for α<1 and is preceded by a broad non-ergodic sub-diffusive phase. Starting from parameters at which the short-range interacting system shows 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 α. Hence, the critical disorder h_c^r, at which ergodic to non-ergodic transition takes place increases with the range of interactions. Time evolution of the density imbalance I(t), which has power-law decay I(t) sim t^-γ in the intermediate to large time regime, shows that the critical disorder h_c^I, above which the system becomes diffusion-less with $γsim 0$ 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 non-ergodic sub-diffusive phase, which is characterized by the Poissonian statistics for the level spacing ratio, multifractal eigenfunctions and a non zero dynamical exponent γll 1/2. The system continues to be sub-diffusive even on the ergodic side $h < h_c^r$ of the MBL transition, where the eigenstates near the mobility edges are multifractal. For h < h₀<h_c^r, the system is super-diffusive with γ>1/2. The rich phase diagram obtained here is unique to 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.