Anomalous dimensions and critical exponents for the Gross-Neveu-Yukawa model at five loops

TL;DR

This paper computes high-order loop corrections to the Gross-Neveu-Yukawa model, providing precise critical exponents relevant for quantum phase transitions in materials like graphene.

Contribution

It advances the understanding of the model by calculating five-loop renormalization group functions and critical exponents, including for specific N values, improving upon previous lower-order results.

Findings

Derived five-loop anomalous dimensions and beta functions.

Provided improved critical exponent estimates for N=1,2,5.

Compared results with conformal bootstrap and other methods.

Abstract

We renormalize the Gross-Neveu-Yukawa model with an $O(N)$ symmetry to $\mathcal{O}(\epsilon^5)$ in $d=4-\epsilon$ dimensions and determine the anomalous dimensions of the fermion and scalar fields, $\beta$-functions as well as the scalar field's mass operator. These are used to construct several $N$ dependent critical exponents relevant for quantum transitions in semi-metals and in particular those connected with graphene in three dimensions when $N=2$. Improved exponent estimates for scalar fermion transitions on a honeycomb lattice, when $N=1$, as well as for $N=5$ are also given to compare with results from other techniques such as the conformal bootstrap.