Four-loop critical exponents for the Gross-Neveu-Yukawa models

We study the chiral Ising, the chiral XY, and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in $4-\epsilon$ dimensions and compute critical exponents for the Gross-Neveu-Yukawa fixed points to order $\mathcal{O}({\epsilon }^4)$. Further, we provide Padé estimates for the correlation length exponent, the boson and fermion anomalous dimension, as well as the leading correction to scaling exponent in $2+1$ dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with $N=1/4$ and $N=1/2$ fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.

Figure 1

Sample diagrams contributing to the fermion-fermion-scalar renormalization in $D=3$ dimensions. The scalar field is denoted $\varphi$ and the Majorana fermions $\mathrm{\Psi }$.