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

TL;DR

This paper calculates four-loop critical exponents for Gross-Neveu-Yukawa models using perturbative renormalization group methods, providing high-precision estimates relevant for quantum phase transitions in materials.

Contribution

It presents the first four-loop order calculations of critical exponents for these models and confirms supersymmetry emergence at this order.

Findings

Critical exponents computed to order ε^4.

Padé estimates for 2+1 dimensions.

Confirmation of supersymmetry at four loops.

Abstract

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 Pad\'e 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.