Deconfined criticality from the QED$_3$-Gross-Neveu model at three loops

TL;DR

This paper analyzes the critical behavior of the QED$_3$-Gross-Neveu model in 2+1 dimensions using a three-loop epsilon expansion, providing estimates for critical exponents and supporting duality with a four-fermion gauge theory.

Contribution

It offers a three-loop epsilon expansion analysis of the QED$_3$-Gross-Neveu model, deriving critical exponents and evidence for duality with a four-fermion gauge theory.

Findings

Critical exponents estimated via Pade approximants.

Scaling relation consistent with SO(5) symmetry.

Evidence supporting duality with a four-fermion gauge theory.

Abstract

The QED$_3$-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory involving Dirac fermions and a critical real scalar field. This theory has recently been argued to represent a dual description of the deconfined quantum critical point between Neel and valence bond solid orders in frustrated quantum magnets. We study the critical behavior of the QED$_3$-Gross-Neveu model by means of an epsilon expansion around the upper critical space-time dimension of $D_c^+=4$ up to the three-loop order. Estimates for critical exponents in 2+1 dimensions are obtained by evaluating the different Pade approximants of their series expansion in epsilon. We find that these estimates, within the spread of the Pade approximants, satisfy a nontrivial scaling relation which follows from the emergent SO(5) symmetry implied by the duality conjecture. We also construct explicit evidence for the equivalence between the QED$_3$-Gross-Neveu model and a corresponding critical four-fermion gauge theory that was previously studied within the 1/N expansion in space-time dimensions 2<D<4.