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

• Published in: Physical review research 2020-03, Vol.2 (1), p.012074, Article 012074
• Main Authors: Modak, Ranjan, Nag, Tanay
• Format: Article
• Language: English
• ISSN: 2643-1564; 2643-1564
• DOI: 10.1103/PhysRevResearch.2.012074

Much has been learned about universal properties of entanglement entropy (EE) and participation ration (PR) for Anderson localization. We find a new subextensive 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 the presence of correlated disorder, an admixture of two species of SPSs (ergodic delocalized and nonergodic multifractal or localized) are observed, which leads to extensive (subextensive) 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 the uncorrelated case there exists only primary growth followed by the saturation. We believe that our findings from the typical many-body eigenstate would remain unaltered even in the weakly interacting limit.