Kekule quantum criticality from Dirac fermion fluctuations: a functional RG approach

We consider a system of Dirac fermions coupled to a Z3 order parameter field as it occurs in the Kekule valence bond solid on the honeycomb lattice. From Landau-Ginzburg paradigm, a discontinuous nature of the corresponding phase transition is expected due to the possibility of cubic terms in the free energy. This, however, has been challenged by scaling corrections due to fermionic quantum fluctuations (arXiv:1609.03208, arXiv:1610.07603). We study the modifications of scaling and the fixed point structure of a Gross-Neveu-Yukawa theory for this system employing the non-perturbative functional renormalization group. This enables a direct evaluation of critical behavior in 2+1 dimensions for an arbitrary number of fermions and provides access to non-perturbative information of the scalar effective potential.