Ensemble Inequivalence in Long-Range Quantum Spin Systems

Ensemble inequivalence occurs when a systems thermodynamic properties vary depending on the statistical ensemble used to describe it. This phenomenon is known to happen in systems with long-range interactions and has been observed in many classical systems. In this study, we provide a detailed analysis of a long-range quantum ferromagnet spin model that exhibits ensemble inequivalence. At zero temperature ($T = 0$), the microcanonical phase diagram matches that of the canonical ensemble. However, the two ensembles yield different phase diagrams at finite temperatures. This behavior contrasts with the conventional understanding in statistical mechanics of systems with short-range interactions, where thermodynamic properties are expected to align across different ensembles in the thermodynamic limit. We discuss the implications of these findings for synthetic quantum long-range platforms, such as atomic, molecular, and optical (AMO) systems.