Level statistics of the disordered Haldane-Shastry model with $1/r^\alpha$ interaction

TL;DR

This study investigates how long-range interactions and different types of disorder influence level statistics in a disordered Haldane-Shastry model, revealing conditions under which many-body localization emerges.

Contribution

It demonstrates that Poisson level statistics, indicative of many-body localization, arise only when both position disorder and random magnetic fields are present together in the long-range interacting system.

Findings

Poisson statistics emerge only with combined disorder types.

Breaking SU(2) symmetry affects the role of position disorder.

Scaling collapse of gap ratios depends on the product of interaction range and disorder strength.

Abstract

Understanding how the interaction range and various types of disorder affect the level statistics of many-body quantum systems and lead to the emergence of many-body localization (MBL) is a challenging open frontier. We study the level statistics of a variant of the spin-$1/2$ Haldane-Shastry model with $1/r^{\alpha}$ interactions, where $\alpha{\geq}0$ parametrizes the range of the interactions, in the presence of position disorder and/or random magnetic fields. We find that neither position disorder nor random magnetic fields alone yields pristine Poisson statistics in this long-range interacting system; however, Poisson statistics emerge in their combined presence, suggesting the emergence of MBL when both types of disorder coexist. Interestingly, once random magnetic fields break the $SU(2)$ symmetry, the strength of the position disorder, $\delta$, appears to play an important role, as evidenced by an approximate scaling collapse of the disorder-averaged gap ratios that is parametrized in terms of a single parameter, $\alpha \delta$.