Instabilities of a Generalized Gross-Neveu Quantum Criticality

TL;DR

This paper investigates the stability of a generalized Gross-Neveu quantum critical point, revealing how strong fermion renormalization influences the emergence of superconducting and charge-neutral phases, and the robustness of pairing.

Contribution

It provides an exact analysis of instabilities at a conformal critical point using conformal field theory, highlighting the role of fermion anomalous dimensions.

Findings

Superconducting and charge-neutral phases destabilize the critical point at high fermion anomalous dimensions.

Higher anomalous dimensions increase the critical time-reversal-symmetry breaking needed to suppress superconductivity.

Stronger renormalization enhances the robustness of pairing in the system.

Abstract

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.