Confinement transition in the QED₃-Gross-Neveu-XY universality class

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. In this talk, I will discuss a confinement transition in a system of N_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 QED₃-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−ε space-time dimensions. The consistency between numerical and analytical results is revealed from large to intermediate flavor number.

References: L. Janssen, W. Wang, M. M. Scherer, Z. Y. Meng, and X. Y. Xu, Phys. Rev. B 101, 235118 (2020).