Toward a Complexity Classification of High-Temperature Bosons: Computational Tractability and Power-Law Clustering
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908750036598784 |
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| author | Tong, Xin-Hai Kuwahara, Tomotaka |
| author_facet | Tong, Xin-Hai Kuwahara, Tomotaka |
| contents | Determining when quantum many-body systems admit simple, efficiently simulable structure is a central problem. High-temperature thermal states are a natural candidate for such simplicity, yet for bosons, the unbounded local Hilbert space and energy invalidate the usual expectation that large $T$ guarantees tractability. Here we investigate the resulting complexity boundary for interacting lattice bosons and show that the repulsive Bose--Hubbard class lies on the ``simple'' side. For a family with long-range hopping decaying as $r^{-α}$, we prove convergence of a controlled cluster expansion, which implies (above an explicit temperature threshold) an efficient classical algorithm to approximate the partition function and a rigorous power-law clustering bound for connected correlations. More broadly, our results provide a first step toward charting complexity boundaries for high-temperature bosons and suggest the repulsive Bose--Hubbard class as a natural candidate cusp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25572 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toward a Complexity Classification of High-Temperature Bosons: Computational Tractability and Power-Law Clustering Tong, Xin-Hai Kuwahara, Tomotaka Quantum Physics Statistical Mechanics Mathematical Physics Determining when quantum many-body systems admit simple, efficiently simulable structure is a central problem. High-temperature thermal states are a natural candidate for such simplicity, yet for bosons, the unbounded local Hilbert space and energy invalidate the usual expectation that large $T$ guarantees tractability. Here we investigate the resulting complexity boundary for interacting lattice bosons and show that the repulsive Bose--Hubbard class lies on the ``simple'' side. For a family with long-range hopping decaying as $r^{-α}$, we prove convergence of a controlled cluster expansion, which implies (above an explicit temperature threshold) an efficient classical algorithm to approximate the partition function and a rigorous power-law clustering bound for connected correlations. More broadly, our results provide a first step toward charting complexity boundaries for high-temperature bosons and suggest the repulsive Bose--Hubbard class as a natural candidate cusp. |
| title | Toward a Complexity Classification of High-Temperature Bosons: Computational Tractability and Power-Law Clustering |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2509.25572 |