Effects of Flip–Flop Interactions and Dissipation in Quantum Critical Light–Matter Systems

We investigate quantum phase transitions in a minimal light–matter platform in the presence of matter-matter interaction: two qubits coupled to a single bosonic mode and mutually interacting via a flip–flop exchange. In the closed system, the competition between the exchange interactions and the light–matter coupling reshapes the conventional superradiant criticality, leading to interaction-tunable critical boundaries and qualitative changes in the nature of the transition. We then extend the study to an open-system setting by coupling the cavity and qubits to dissipative environments described by a Lindblad master equation. Focusing on the steady state and low-lying Liouvillian spectrum, we analyze how dissipation and dephasing modify equilibrium critical points, including the emergence of nonequilibrium crossovers and, in suitable regimes, genuinely dissipative critical behavior. We further discuss how dissipation reorganizes quantum correlations across the critical region and identify parameter windows where interactions and dissipation jointly enhance or suppress nonclassical features. Our results provide a unified equilibrium-to-nonequilibrium perspective on interaction-engineered critical phenomena in few-qubit Rabi architectures, with direct relevance to circuit QED and trapped ion implementations.