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We study the quantum phase diagram and the onset of quantum criticalphenomena in a generalized Dicke model that includes collective qubit-qubitinteractions. By employing semiclassical techniques, we analyze thecorresponding classical energy surfaces, fixed points, and the smooth Densityof States as a function of the Hamiltonian parameters to determine quantumphase transitions in either the ground (QPT) or excited states (ESQPT). Weunveil a rich phase diagram, the presence of new phases, and new transitionsthat result from varying the strength of the qubits interactions in independentcanonical directions. We also find a correspondence between the phases emergingdue to qubit interactions and those in their absence but with varying thestrength of the non-resonant terms in the light-matter coupling. We expect ourwork to pave the way and stimulate the exploration of quantum criticality insystems combining matter-matter and light-matter interactions.

Critical phenomena in light-matter systems with collective matter interactions