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Effect of short-range interactions on the quantum critical behavior of spinless fermions on the honeycomb lattice

We present a functional renormalization group investigation of an Euclidean three-dimensional matrix Yukawa model with U(N) symmetry, which describes N = 2 Weyl fermions that effectively interact via a short-range repulsive interaction. This system relates to an effective low-energy theory of spinless electrons on the honeycomb lattice and can be seen as a simple model for suspended graphene. We find a continuous phase transition characterized by large anomalous dimensions for the fermions and composite degrees of freedom. The critical exponents define a new universality class distinct from Gross-Neveu type models, typically considered in this context.