Although the superradiant phase transition (SRPT) is prohibited in the paradigmatic quantum Rabi model due to the no-go theorem caused by the
A2 term, we demonstrate two distinct types of SRPTs emerging from the normal phase in the anisotropic quantum Rabi model. A discontinuous phase transition between the two types of superradiant phases also emerges in the presence of a strong
A2 term. Additionally, a rich phase diagram featuring a triple point, which connects first- and second-order phase transitions, is derived analytically and confirmed through numerical diagonalization at large effective system sizes. Finally, distinct critical behavior at the triple point is revealed and contrasted with that of a single continuous SRPT. This work may open a new avenue for observing SRPTs in their intrinsic form without altering the
A2 term, while also offering a practical platform for exploring rich quantum phenomena.
Equilibrium phase transitions between a normal and a photon condensate state (also known as superradiant phase transitions) are a highly debated research topic, where proposals for their occurrence and no-go theorems have chased each other for the past four decades. Previous no-go theorems have demonstrated that gauge invariance forbids second-order phase transitions to a photon condensate state when the cavity-photon mode is assumed to be spatially uniform. First-order phase transitions were previously considered as possible paths to bypass the no-go theorem. In particular, it has been theoretically predicted that a collection of three-level systems coupled to light can display a first-order phase transition to a photon condensate state. Here, we lay down a general no-go theorem, which forbids first-order as well as second-order superradiant phase transitions in a spatially-uniform cavity field. By using the tools of lattice gauge theory, we then derive a fully gauge-invariant model for three-level systems coupled to light. In agreement with the general theorem, our model does not display photon condensation.