Level statistics of the disordered Haldane-Shastry model with $1/r^α$ interaction
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| Format: | Preprint |
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2026
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| author | Ganapathy, Vengatesan Patil, Pranay Balram, Ajit C. |
| author_facet | Ganapathy, Vengatesan Patil, Pranay Balram, Ajit C. |
| contents | 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, $αδ$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_14695 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Level statistics of the disordered Haldane-Shastry model with $1/r^α$ interaction Ganapathy, Vengatesan Patil, Pranay Balram, Ajit C. Strongly Correlated Electrons Statistical Mechanics Quantum Physics 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, $αδ$. |
| title | Level statistics of the disordered Haldane-Shastry model with $1/r^α$ interaction |
| topic | Strongly Correlated Electrons Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2604.14695 |