Critical properties of antiferromagnetic and valence-bond-solid transitions in lattice quantum electrodynamics

Lattice gauge theories underlie the effective low-energy description of many strongly correlated electron systems, such as frustrated magnets and high-temperature superconductors, but can now also be simulated directly in cold atom experiments. Elucidating the phase diagram of lattice gauge theories is thus an important problem with a wide range of applications to condensed matter physics. Recent sign-problem-free quantum Monte Carlo simulations of lattice quantum electrodynamics (QED) with N flavors of fermions on the square lattice have found evidence of continuous quantum phase transitions between a critical deconfined phase at small gauge coupling and confined antiferromagnetic (for N=2) or valence-bond-solid (for N=4,6,8) phases at large gauge coupling. We derive Landau-Ginzburg-Wilson theories of the QED-Gross-Neveu(-Yukawa) type for these transitions, find stable renormalization-group fixed points corresponding to the observed quantum critical points, and compute their critical exponents using epsilon and large-N expansions.