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Overlap with the separable state is introduced in this paper for the purposeof characterizing the overall correlation in many-body systems. This definitionhas clear geometric and physical meaning, and moreover can be considered as thegeneralization of the concept-Anderson Orthogonality Catastrophe. As anexemplification, it is used to mark the phase transition in the Dicke model forzero and finite temperature. And our discussion shows that it can faithfullyreflect the phase transition properties of this model whether for zero orfinite temperature. Furthermore the overlap for ground state also indicates theappearance of multipartite entanglement in Dicke model.

Overlap with the Separable State and Phase Transition in the Dicke Model: Zero and Finite Temperature