High-temperature partition functions and classical simulability of long-range quantum systems

• URL: http://arxiv.org/abs/2504.20901v1
• Date: Tue, 29 Apr 2025 16:17:45 GMT
• Title: High-temperature partition functions and classical simulability of long-range quantum systems
• Authors: Jorge Sánchez-Segovia, Jan T. Schneider, Álvaro M. Alhambra,
• Abstract summary: We study fundamental properties of long-range spin systems in thermal equilibrium.<n>Our main result is a proof of analiticity of their partition functions at high temperatures.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, 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 $ \alpha>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 $\exp(\mathcal{O}(\log^2(N/\epsilon)))$ that approximates the log-partition function to small additive error $\epsilon$. 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 Koteck\'y and Preiss.

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