Gross-Neveu-Heisenberg criticality from 2+ expansio br

The Gross-Neveu-Heisenberg universality class describes a continuous quantum phase transition between aDirac semimetal and an antiferromagnetic insulator. Such quantum critical points have originally been discussedin the context of Hubbard models on pi-flux and honeycomb lattices, but more recently also in Bernal-stackedbilayer models, of potential relevance for bilayer graphene. Here, we demonstrate how the critical behavior ofthis fermionic universality class can be computed within an expansion around the lower critical space-timedimension of two. This approach is complementary to the previously studied expansion around the uppercritical dimension of four. The crucial technical difference near the lower critical dimension is the presence ofdifferent four-fermion interaction channels at the critical point, which we take into account in a Fierz-completeway. By interpolating between the lower and upper critical dimensions, we obtain improved estimates forthe critical exponents in 2+1 space-time dimensions. For the situation relevant to single-layer graphene, wefind an unusually small leading-correction-to-scaling exponent, arising from the competition between differentinteraction channels. This suggests that corrections to scaling may need to be taken into account when comparinganalytical estimates with numerical data from finite-size extrapolations