Multi-critical behavior of $Z_2\times O(2)$ Gross-Neveu-Yukawa theory in graphene

TL;DR

This paper investigates the multi-critical behavior of interacting fermions in graphene, showing that certain symmetry-breaking terms are irrelevant near critical points and that Yukawa couplings enhance stability.

Contribution

It introduces a Gross-Neveu-Yukawa theoretical framework to analyze symmetry-breaking effects and stability of critical points in graphene's fermionic system.

Findings

Symmetry-breaking terms are irrelevant near the critical point.

Finite Yukawa coupling stabilizes the critical point.

Critical exponents are calculated for the transitions.

Abstract

Multi-critical behavior of interacting fermions in graphene's honeycomb lattice is presented. In particular, we considered the spin triplet insulating orders, where the spin rotational symmetry of the order parameter is explicitly broken. By casting the problem in terms of Gross-Neveu-Yukawa theory we show that such symmetry-breaking terms are irrelevant near the metal-insulator critical point. A finite Yukawa coupling among bosons and fermions improves the stability of such critical point against the symmetry-breaking perturbations. Physical sources of such symmetry-breaking terms are pointed out. Critical exponents are calculated near the transitions as well.