How does entanglement entropy serve as an order parameter in quantum phase transitions, and what insights does it provide compared to classical order parameters?

Entanglement entropy measures the quantum correlations between different parts of a system and can signal quantum phase transitions where traditional order parameters may not. It provides insights into the critical behavior and universality classes of quantum systems, revealing new phases of matter that are not identifiable through classical order parameters, especially in systems with topological order or where symmetry breaking is absent.