Critical behavior of the QED$_3$-Gross-Neveu-Yukawa model at four loops

TL;DR

This paper computes critical exponents and scaling dimensions of the QED$_3$-Gross-Neveu-Yukawa model at four-loop order, providing insights into quantum phase transitions relevant for antiferromagnets and spin liquids.

Contribution

It presents a four-loop epsilon expansion analysis of the model's critical properties, including anomalous dimensions and scaling dimensions, for various N values.

Findings

Determines critical exponents for N=1 and N=2 cases.

Provides estimates of critical properties in 2+1 dimensions using Padé approximants.

Connects the model to deconfined quantum critical points and spin liquid transitions.

Abstract

We study the universal critical properties of the QED$_3$-Gross-Neveu-Yukawa model with $N$ flavors of four-component Dirac fermions coupled to a real scalar order parameter at four-loop order in the $\epsilon$ expansion below four dimensions. For $N=1$, the model is conjectured to be infrared dual to the $SU(2)$-symmetric noncompact $\mathbb{C}$P$^1$ model, which describes the deconfined quantum critical point of the N\'eel-valence-bond-solid transition of spin-1/2 quantum antiferromagnets on the two-dimensional square lattice. For $N=2$, the model describes a quantum phase transition between an algebraic spin liquid and a chiral spin liquid in the spin-1/2 kagom\'e antiferromagnet. For general $N$ we determine the order parameter anomalous dimension, the correlation length exponent, the stability critical exponent, as well as the scaling dimensions of $SU(N)$ singlet and adjoint fermion mass bilinears at the critical point. We use Pad\'e approximants to obtain estimates of critical properties in 2+1 dimensions.