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

• URL: http://arxiv.org/abs/2604.14695v1
• Date: Thu, 16 Apr 2026 06:55:41 GMT
• Title: Level statistics of the disordered Haldane-Shastry model with $1/r^α$ interaction
• Abstract summary: We study the level statistics of a variant of the spin-$1/2$ Haldane-Shastry model with $1/r$ interactions.<n>We find that neither position disorder nor random magnetic fields alone yields pristine Poisson statistics.<n>However, Poisson statistics emerge in their combined presence, suggesting the emergence of MBL when both types of disorder coexist.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $1/r^α$ 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 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, $δ$, 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, $αδ$.

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