Critical properties of entanglement in the Dicke model with the dipole–dipole interactions

In this paper, we investigate two aspects of entanglement properties of the ground state for the Dicke model with the dipole–dipole interaction between the atoms in the thermodynamic limit, and observe how they are affected by the quantum phase transition. The appearance of dipole–dipole interactions between the atoms does not change the maximum atom–field entanglement at the critical point, while it changes the maximum atom–atom entanglement at the critical point, and has an important influence on the atom–atom entanglement behavior.