Fermion-induced quantum criticality with two length scales in Dirac systems

The quantum phase transition to a Z(3)-ordered Kekule valence bond solid in two-dimensional Dirac semimetals is governed by a fermion-induced quantum critical point, which renders the putatively discontinuous transition continuous. We study the resulting universal critical behavior in terms of a functional RG approach, which gives access to the scaling behavior on the symmetry-broken side of the phase transition, for general dimensions and number of Dirac fermions. In particular, we investigate the emergence of the fermion-induced quantum critical point for spacetime dimensions 2 < D < 4. We determine the integrated RG flow from the Dirac semimetal to the symmetry-broken regime and analyze the underlying fixed-point structure. We show that the fermion-induced criticality leads to a scaling form with two divergent length scales, due to the breaking of the discrete Z(3) symmetry. This provides another source of scaling corrections, besides the one stemming from being in the proximity to the first-order transition