  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.
