Boundary criticality for the Gross-Neveu-Yukawa models

We study the boundary criticality for the Gross-Neveu-Yukawa (GNY) models. Employing interacting Dirac fermions on a honeycomb lattice with armchair boundaries, we use determinant quantum Monte Carlo simulation to uncover rich boundary criticalities at the quantum phase transition to a charge density wave (CDW) insulator, including the ordinary, special, and extraordinary transitions. The Dirac fermions satisfy a Dirichlet boundary condition, while the boson field, representing the CDW order, obeys Dirichlet and Neumann conditions at the ordinary and special transitions, respectively, thereby enriching the critical GNY model. We develop a perturbative $4-\epsilon$ renormalization group approach to compute the boundary critical exponents. Our framework generalizes to other GNY universality class variants and provides theoretical predictions for experiments.