# Deconfined criticality in the QED$_{3}$ Gross-Neveu-Yukawa model: The $1/N$ expansion revisited

## TL;DR

This paper revisits the critical properties of the QED$_{3}$ Gross-Neveu-Yukawa model in 2+1 dimensions using a $1/N$ expansion, highlighting the importance of previously overlooked diagrams and supporting a duality conjecture with numerical results.

## Contribution

It introduces the inclusion of Aslamazov-Larkin diagrams in the $1/N$ expansion analysis of the QED$_{3}$ GNY model, improving the accuracy of critical exponent predictions.

## Key findings

- Resummed scaling dimensions align with numerical studies.
- Aslamazov-Larkin diagrams significantly affect operator scaling.
- Supports the duality between the QED$_{3}$ GNY critical point and N{é}el-VBS transition.

## Abstract

The critical properties of the QED$_{3}$ Gross-Neveu-Yukawa (GNY) model in 2+1 dimensions with $N$ flavors of two-component Dirac fermions are computed to first order in the $1/N$ expansion. For the specific case of $N=2$, the critical point is conjectured to be dual to the N\'eel-to-valence-bond-solid (VBS) deconfined critical point of quantum antiferromagnets on the square lattice. It is found that Aslamazov-Larkin diagrams, missed by previous $\epsilon$- and $1/N$-expansion studies with four-component fermions, give important contributions to the scaling dimensions of various operators. With the inclusion of these diagrams, the resummed scaling dimensions of the adjoint fermion bilinear and scalar field at the QED$_{3}$ GNY critical point are in reasonable agreement with numerical studies of the N\'eel-to-VBS transition, in support of the duality conjecture.