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The coupling between fermionic matter and gauge fields plays a fundamentalrole in our understanding of nature, while at the same time posing achallenging problem for theoretical modeling. In this situation, controlledinformation can be gained by combining different complementary approaches.Here, we study a confinement transition in a system of $N_f$ flavors ofinteracting Dirac fermions charged under a U(1) gauge field in 2+1 dimensions.Using Quantum Monte Carlo simulations, we investigate a lattice model thatexhibits a continuous transition at zero temperature between a gaplessdeconfined phase, described by three-dimensional quantum electrodynamics, and agapped confined phase, in which the system develops valence-bond-solid order.We argue that the quantum critical point is in the universality class of theQED$_3$-Gross-Neveu-XY model. We study this field theory within a $1/N_f$expansion in fixed dimension as well as a renormalization group analysis in$4-\epsilon$ space-time dimensions. The consistency between numerical andanalytical results is revealed from large to intermediate flavor number.

Confinement transition in the QED$_3$-Gross-Neveu-XY universality class