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arXiv:2010.12485 · Physical review. B./Physical review. B

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

Yogeshwar Prasad, Arti Garg

Published Feb 8, 2021• 17 citations
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Abstract

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 ${V}_{ij}/{({r}_{ij})}^{\ensuremath{\alpha}}$ with distance ${r}_{ij}$. We demonstrate that MBL survives even for $\ensuremath{\alpha}<1$ 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 $\ensuremath{\alpha}$. 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 $I(t)\ensuremath{\sim}{t}^{\ensuremath{-}\ensuremath{\gamma}}$ in the intermediate to large time regime, shows that the critical disorder ${h}_{c}^{I}$, above which the system becomes diffusionless (with $\ensuremath{\gamma}\ensuremath{\sim}0$) 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 nonergodic subdiffusive phase, which is characterized by the Poissonian statistics for the level spacing ratio, multifractal eigenfunctions, and a nonzero dynamical exponent $\ensuremath{\gamma}\ensuremath{\ll}1/2$. 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 $\ensuremath{\gamma}>1/2$. 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.

DOI
10.1103/physrevb.103.064203

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