Ensemble inequivalence in long-range quantum spin systems

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 ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>T</a:mi> <a:mo>=</a:mo> <a:mn>0</a:mn> </a:mrow> </a:math> ), 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.