Deconfined quantum criticality from the $\mathrm{QED}_{3}$-Gross-Neveu-Yukawa model: the $1/N$ expansion revisited

Quantum phase transitions involving dynamical gauge fields are an important class of transitions beyond the standard Landau-Ginzburg-Wilson paradigm. Two subcategories are those where (i) the gauge field deconfines only at the critical point itself, and (ii) the gauge field deconfines in one of the phases separated by the critical point. The latter subcategory is exemplified by the $\mathrm{QED}_{3}$-Gross-Neveu-Yukawa (GNY) model in which there has been great interest recently due to a conjecture relating its critical point to the N\'eel-to-valence-bond-solid (VBS) deconfined critical point in the first subcategory. Motivated by this, we use the $1/N$ expansion to study the $\mathrm{QED}_{3}$-GNY model in fixed three spacetime dimensions, with $N$ flavors of two-component Dirac fermions. We find new contributions to critical exponents arising from Aslamazov-Larkin diagrams missed by previous epsilon- and $1/N$-expansion studies in arbitrary dimensions. For the specific case of $N=2$, when the duality is conjectured to hold, we find that the bosonic anomalous dimension and adjoint fermion bilinear scaling dimension are in reasonable agreement with numerical studies of the N\'eel-to-VBS transition.