Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality

Abstract

We study the critical properties of the QED${}_3$-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 CP${}^1$ model that describes the deconfined phase transition between the Neel 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 QED${}_3$-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 QED${}_3$ (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 $\epsilon =4-D$. We compute the scalar-field anomalous dimension ${\eta }_{\varphi }$, the correlation-length exponent $\nu$, as well as the scaling dimension of the flavor-symmetry-breaking bilinear $\bar{\psi }{\sigma }^z\psi$ at the critical point, and compare our leading-order estimates with predictions of the conjectured duality.

arXiv comment12 pages, 7 figures, 1 table; v2: loop diagrams added, additional comments and references, published version

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