Quantum phase transition for the Dicke model with the dipole–dipole interactions

In this paper, we reveal a second-order phase transition for the Dicke model with the dipole–dipole interaction between the atoms. By means of Holstein–Primakoff transformation, the energy spectra for both the normal and superradiant phases are explicitly obtained and therefore the scaling behaviour near the critical transition point can be given clearly. It is also shown that the dipole–dipole interactions between the atoms deeply affect the critical transition point, the ground-state and excitation energies and the scaled atomic inversion in the ground state.