High-temperature partition functions and classical simulatability of long-range quantum systems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917188116414464 |
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| author | Sánchez-Segovia, Jorge Schneider, Jan T. Alhambra, Álvaro M. |
| author_facet | Sánchez-Segovia, Jorge Schneider, Jan T. Alhambra, Álvaro M. |
| contents | Long-range quantum systems, in which the interactions decay as $1/r^α$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of long-range spin systems in thermal equilibrium, focusing on the weak regime of $ α>D$. Our main result is a proof of analiticity of their partition functions at high temperatures, which allows us to construct a classical algorithm with sub-exponential runtime $\exp(\mathcal{O}(\log^2(N/ε)))$ that approximates the log-partition function to small additive error $ε$. As by-products, we establish the equivalence of ensembles and the Gaussianity of the density of states, which we verify numerically in both the weak and strong long-range regimes. This also yields constraints on the appearance of various classes of phase transitions, including thermal, dynamical and excited-state ones. Our main technical contribution is the extension to the quantum long-range regime of the convergence criterion for cluster expansions of Kotecký and Preiss. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-temperature partition functions and classical simulatability of long-range quantum systems Sánchez-Segovia, Jorge Schneider, Jan T. Alhambra, Álvaro M. Quantum Physics Statistical Mechanics Long-range quantum systems, in which the interactions decay as $1/r^α$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of long-range spin systems in thermal equilibrium, focusing on the weak regime of $ α>D$. Our main result is a proof of analiticity of their partition functions at high temperatures, which allows us to construct a classical algorithm with sub-exponential runtime $\exp(\mathcal{O}(\log^2(N/ε)))$ that approximates the log-partition function to small additive error $ε$. As by-products, we establish the equivalence of ensembles and the Gaussianity of the density of states, which we verify numerically in both the weak and strong long-range regimes. This also yields constraints on the appearance of various classes of phase transitions, including thermal, dynamical and excited-state ones. Our main technical contribution is the extension to the quantum long-range regime of the convergence criterion for cluster expansions of Kotecký and Preiss. |
| title | High-temperature partition functions and classical simulatability of long-range quantum systems |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2504.20901 |