Deconfined criticality in the ${\mathrm{QED}}_3$ Gross-Neveu-Yukawa model: The $1/N$ expansion revisited

The critical properties of the ${\mathrm{QED}}_3$ 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 Néel-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 ${\mathrm{QED}}_3$ GNY critical point are in reasonable agreement with numerical studies of the Néel-to-VBS transition, in support of the duality conjecture.

Figure 1

Resummed propagators in the large-$N$ formalism for (a) the gauge field and (b) the scalar field. Solid lines denote bare fermion propagators, and single wiggly and dashed lines denote bare gauge and scalar propagators, respectively. Double wiggly and dashed lines represent the resummed gauge and scalar propagators, respectively.

Figure 2

Vanishing contributions to the gauge and scalar propagators.

Figure 3

Propagators and vertices in the large-$N$ formalism. (a) The bare fermion propagator; (b) and (c) the large-$N$ gauge and scalar propagators, respectively; and (d) and (e) the large-$N$ vertices for the gauge and scalar interactions with the bare fermions, respectively.

Figure 4

Lowest-order $\left[O\left(N^0\right)\right]$ contribution to the fermion four-point correlation function. The $\times$ denotes the prefactor $1/\sqrt{N}$.

Figure 5

The $O(1/N)$ corrections to the fermion four-point correlation function in pure ${\mathrm{QED}}_3$. The Aslamazov-Larkin diagrams in (d) and (e) vanish for the adjoint bilinear.

Figure 6

The $O(1/N)$ corrections to the fermion four-point correlation function in pure GNY. The Aslamazov-Larkin diagrams in (d) and (e) vanish identically.

Figure 7

The $O(1/N)$ corrections to the fermion four-point correlation function with gauge and scalar propagators.

Figure 8

(a) The Dyson equation and its $O(1/N)$ solution for the bosonic two-point correlation function $G_{\varphi }$. (b) Scalar self-energy diagrams that contribute at $O(1/N)$.

Figure 9

Scalar bubble contributions to the scalar four-point function.

Figure 10

Fermion box contributions to the scalar four-point function.

Figure 11

Example of an $O(1/N^2)$ correction to the fermion four-point function from ${\mathrm{QED}}_3$ AL subdiagrams.