Critical Property of Geometric Phase in the Dicke Model

Abstract

We obtain the ground-state energy level and associated geometric phase in the Dicke model analytically by means of the Holstein-Primakoff transformation and the boson expansion approach in the thermodynamic limit. The non-adiabatic geometric phase induced by the photon field is derived with the time-dependent unitary transformation. It is shown that the quantum phase transition characterized by the non-analyticity of the geometric phase is remarkably of the first-order. We also investigate the scaling behavior of the geometric phase at the critical point, which can be measured in a practical experiment to detect the quantum phase transition.

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References in corpus (4)

• Geometric phases and criticality in spin chain systems
• Adiabatic Geometric Phase for a General Quantum States
• Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement
• Scaling of Berry's Phase Close to the Dicke Quantum Phase Transition

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