Quantum phase transitions in the Lipkin-Meshkov-Glick model via mutual information within Husimi phase space representation

This research demonstrates that entropy-based measures, calculated from marginals of the Husimi functions, effectively identify and characterize quantum phase transitions in the Lipkin-Meshkov-Glick model. The study reveals that changes in entropy, particularly Wehrl entropy, marginal entropies, and mutual information, act as sensitive indicators of criticality, distinguishing between different transition orders and highlighting the breakdown of separability near critical points. These findings establish entropy analysis as a powerful, complementary tool to traditional methods for understanding quantum criticality in many-body systems.