# Many-body dynamics in long-range hopping model in the presence of correlated and uncorrelated disorder

## TL;DR

This paper investigates how entanglement entropy and participation ratio scale in long-range hopping models with disorder, revealing new sub-extensive behaviors and the effects of correlated versus uncorrelated disorder on many-body dynamics.

## Contribution

It uncovers the scaling behavior of EE and PR in long-range models with disorder, highlighting the impact of correlations and the nature of single-particle states on many-body eigenstates.

## Key findings

- Sub-extensive scaling of EE and PR in algebraic localization.
- Universal variation of EE scaling exponent with localization exponent.
- Secondary slow growth of EE observed only in correlated disorder cases.

## Abstract

Much have been learned about universal properties of entanglement entropy (EE) and participation ration (PR) for Anderson localization. We find a new sub-extensive scaling with system size of the above measures for algebraic localization as noticed in one-dimensional long-range hopping models in the presence of uncorrelated disorder. While the scaling exponent of EE seems to vary universally with the long distance localization exponent of single particle states (SPSs), PR does not show such university as it also depends on the short range correlations of SPSs. On the other hand, in presence of correlated disorder, an admixture of two species of SPSs (ergodic delocalized and non-ergodic multifractal or localized) are observed, which leads to extensive (sub-extensive) scaling of EE (PR). Considering typical many-body eigenstates, we obtain above results that are further corroborated with the asymptotic dynamics. Additionally, a finite time secondary slow growth in EE is witnessed only for correlated case while for uncorrelated case there exists only primary growth followed by the saturation. We believe that our findings from typical many-body eigenstate would remain unaltered even in the weakly interacting limit.