Spin coherent-state transformation and analytical solutions of ground-state based on variational-method for spin-Bose models

We present a variational method for the ground-state solutions of the spin-Bose models by means of the spin coherent-state transformation. For the Jaynes-Cummings (J-C) models with and without the rotating-wave approximation, the ground-state energies obtained by this method are in perfect agreement with the results from numerical diagonalization in the whole region of the coupling between a light field and an atom. The present variational-method can be directly used to solve the ground-state energies of the Dicke models with arbitrary atom-numbers and furoher study the quantum phase transition; while the variational-method based on the Holstein-Primakoff transformation is only valid in principle for the thermodynamic limit with the atom-number tending to infinity.