Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: Scaling of entanglement

We show that the quantum phase transition arising in a standard radiation-matter model (Dicke model) belongs to the same universality class as the infinitely coordinated, transverse-field XY model. The effective qubit-qubit exchange interaction is shown to be proportional to the square of the qubit-radiation coupling. A universal finite-size scaling is derived for the corresponding two-qubit entanglement (concurrence) and a size-consistent effective Hamiltonian is proposed for the qubit subsystem.