Coulomb interactions, gauge invariance, and phase transitions of the Dicke model

Phase transitions of a generalized Dicke model in the Coulomb gauge-including A(2) terms in the matter-radiation coupling, as well as direct dipole-dipole interaction terms-are studied. After a brief review of previous work on the 'no-go theorem' for phase transitions in the Dicke model, it is shown that a consistent truncation of the radiation modes and of the direct interactions leads to a model that does have a phase transition. When transformed to the electric dipole gauge, such a system takes exactly the form of the original Dicke Hamiltonian, which displays the expected phase transition.