Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions

Yogeshwar Prasad; Arti Garg

doi:10.1103/PhysRevB.103.064203

paper

Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions

arXiv:2010.12485 · doi:10.1103/PhysRevB.103.064203

Abstract

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 $γ \sim 0$ ) 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 $γ ≪ 1/2$ . 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 $h < h_{0} < h_{c}^{r}$ , 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.

arXiv comment15 pages, 14 figures

Many-body localization and enhanced non-ergodic sub-diffusive regime in the presence of random long-range interactions

Abstract

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