Confinement transition in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>QED</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>-Gross-Neveu-XY universality class
Lukas Janssen, Wei Wang, Michael M. Scherer, Zi Yang Meng, Xiao Yan Xu
Abstract
The coupling between fermionic matter and gauge fields plays a fundamental role in our understanding of nature, while at the same time posing a challenging problem for theoretical modeling. In this situation, controlled information can be gained by combining different complementary approaches. Here, we study a confinement transition in a system of ${N}_{\mathrm{f}}$ flavors of interacting Dirac fermions charged under a U(1) gauge field in $2+1$ dimensions. Using quantum Monte Carlo simulations, we investigate a lattice model that exhibits a continuous transition at zero temperature between a gapless deconfined phase, described by three-dimensional quantum electrodynamics, and a gapped confined phase, in which the system develops valence-bond-solid order. We argue that the quantum critical point is in the universality class of the ${\mathrm{QED}}_{3}$-Gross-Neveu-XY model. We study this field theory within a $1/{N}_{\mathrm{f}}$ expansion in fixed dimension as well as a renormalization group analysis in $4\ensuremath{-}\ensuremath{\epsilon}$ space-time dimensions. The consistency between numerical and analytical results is revealed from large to intermediate flavor number.