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We obtain the ground-state energy level and associated geometric phase in theDicke model analytically by means of the Holstein-Primakoff transformation andthe boson expansion approach in the thermodynamic limit. The non-adiabaticgeometric phase induced by the photon field is derived with the time-dependentunitary transformation. It is shown that the quantum phase transitioncharacterized by the non-analyticity of the geometric phase is remarkably ofthe first-order. We also investigate the scaling behavior of the geometricphase at the critical point, which can be measured in a practical experiment todetect the quantum phase transition.Comment: 1 figur

Critical property of the geometric phase in the Dicke model