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

Vengatesan Ganapathy, Pranay Patil, Ajit C. Balram

Understanding how the interaction range and various types of disorder affect the level statistics of many-body quantum systems, leading 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 $1/r^α$ interactions, where $α{\geq}0$ 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 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, $δ$ , 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, $αδ$ .Understanding how the interaction range and various types of disorder affect the level statistics of many-body quantum systems, leading 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 $1/r^α$ interactions, where $α{\geq}0$ 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 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, $δ$, 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, $αδ$.

cond-mat.str-elCross-listedarXiv:2604.14695Physical review. B./Physical review. BApr 17, 20260 citations

Level statistics of the disordered Haldane-Shastry model with

1/r^α

interaction

1/2

Haldane-Shastry model with

1/r^α

interactions, where

α{\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 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,

δ

, 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,

αδ