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Within the numerically exact solution to the Dicke model proposed previously,we study the quantum criticality in terms of the ground-state (GS) energy,fidelity, and the order parameter. The finite size scaling analysis for theaverage fidelity susceptibility (FS) and second derivative of GS energy areperformed. The correlation length exponent is obtained to be $\nu=2/3$, whichis the same as that in Lipkin-Meshkov-Glick model obtained previously,suggesting the same universality. It is observed that average FS and secondderivative of GS energy show similar critical behavior, demonstrating theintrinsic relation in the Dicke model. The scaling behavior for the orderparameter and the singular part of the GS energy at the critical point are alsoanalyzed and the obtained exponents are consistent with the previous scalinghypothesis in 1/N expansion scheme.

Large-N scaling behavior of the ground-state energy and fidelity in the Dicke Model