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Stability of thermal equilibrium in long-range quantum systems

Tim Möbus1,*, Jorge Sánchez-Segovia2,†, Álvaro M. Alhambra2,‡, and Ángela Capel1,3,§

  • *Contact author: moebustim@gmail.com
  • †Contact author: jorge.sanchezsegovia@estudiante.uam.es
  • ‡Contact author: alvaro.alhambra@csic.es
  • §Contact author: ac2722@cam.ac.uk
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Phys. Rev. Research 8, 013198 – Published 23 February, 2026

DOI: https://doi.org/10.1103/3wbz-lq3p

Abstract

Experimental realizations of spin models are irremediably prone to errors, which can propagate through the system corrupting experimental signals. We study how such errors affect the measurement of local observables in systems with long-range interactions, where perturbations can spread more rapidly. Specifically, we focus on the stability of thermal equilibrium and investigate its relation to the correlation structure of the system, both analytically and numerically. As a main result, we prove that the stability of local expectation values follows from the decay of correlations on the Gibbs state and the Lieb-Robinson bound. We also provide numerical evidence that this stability extends to an even larger regime of interacting long-range systems. Our results support the robustness of analog simulation platforms for long-range models and provide further evidence that computing physical quantities of interest can be significantly easier than performing arbitrary quantum computations.

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Corrections

23 March, 2026

Correction: The citation information given in Ref. [2] was incorrect and has been fixed. Reference [54] and its citation in text were missing and have been inserted.

Article Text

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Phys. Rev. Research 8, 013198– Published 23 February, 2026
  • Received 29 July 2025
  • Accepted 20 January 2026
  • Corrected 23 March 2026
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