Instabilities of a Generalized Gross-Neveu Quantum Criticality

We study the instabilities to the conformal critical point of an exactly solvable family of Gross-Neveu models. Using conformal field theory techniques, we construct the zero-temperature phase diagram and identify the superconducting and charge neutral ordered phases that destabilize the critical point. Both instabilities appear only when the fermions are strongly renormalized, above a critical anomalous dimension. A higher fermion anomalous dimension also raises the critical degree of time-reversal-symmetry breaking required to suppress superconductivity, indicating that pairing becomes more robust with stronger renormalization.