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arXiv:2504.20901 · PRX Quantum

High-Temperature Partition Functions and Classical Simulatability of Long-Range Quantum Systems

Jorge Sánchez-Segovia, Jan T. Schneider, Alvaro Martin Alhambra

Published Nov 17, 2025• 1 citation
arXivHTMLPDF

Abstract

Long-range quantum systems, in which the interactions decay as 1 / r α , are of increasing interest due to the variety of experimental setups 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 analyticity of their partition functions at high temperatures, which allows us to construct a classical algorithm with subexponential runtime exp  ( 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.

DOI
10.1103/cww3-j1vd

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