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Ensemble inequivalence in long-range quantum spin systems

Daniel Arrufat-Vicente1,*, David Mukamel2, Stefano Ruffo3,4,5, and Nicolò Defenu1

  • *Contact author: darrufat@phys.ethz.ch
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Phys. Rev. Research 8, 013333 – Published 27 March, 2026

DOI: https://doi.org/10.1103/hmhz-4g46

Abstract

Ensemble inequivalence, where a system's thermodynamic properties depend on the statistical ensemble used to describe it, is a well-established phenomenon in classical systems with long-range interactions. Here, we present a detailed analysis of a quantum ferromagnet spin model that exhibits this same behavior. We find that the microcanonical and canonical phase diagrams are identical at zero temperature (T=0), but differ significantly at finite temperatures. Our results highlight a breakdown of ensemble equivalence in this quantum long-range model, contrasting with what is observed for short range. These findings have important implications for the study and manipulation of long-range interacting quantum platforms, such as those used in atomic, molecular, and optical physics.

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Phys. Rev. Research 8, 013333– Published 27 March, 2026
  • Received 22 April 2025
  • Accepted 13 January 2026
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