Critical behavior of the QED3 -Gross-Neveu model: Duality and deconfined criticality

We study the critical properties of the QED3-Gross-Neveu model with 2N flavors of two-component Dirac fermions coupled to a massless scalar field and a U(1) gauge field. For N=1, this theory has recently been suggested to be dual to the SU(2) noncompact CP1 model that describes the deconfined phase transition between the Néel antiferromagnet and the valence bond solid on the square lattice. For N=2, the theory has been proposed as an effective description of a deconfined critical point between chiral and Dirac spin liquid phases, and may potentially be realizable in spin-1/2 systems on the kagome lattice. We demonstrate the existence of a stable quantum critical point in the QED3-Gross-Neveu model for all values of N. This quantum critical point is shown to escape the notorious fixed-point annihilation mechanism that renders plain QED3 (without scalar-field coupling) unstable at low values of N. The theory exhibits an upper critical space-time dimension of four, enabling us to access the critical behavior in a controlled expansion in the small parameter ϵ=4-D. We compute the scalar-field anomalous dimension ηφ, the correlation-length exponent ν, as well as the scaling dimension of the flavor-symmetry-breaking bilinear ψσzψ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.