Gross-Neveu Heisenberg criticality: Dynamical generation of quantum spin Hall masses

Abstract

We consider fermions on a honeycomb lattice supplemented by a spin invariant interaction that dynamically generates a quantum spin Hall insulator. This lattice model provides an instance of Gross-Neveu Heisenberg criticality, as realized for example by the Hubbard model on the honeycomb lattice. Using auxiliary field quantum Monte Carlo simulations we show that we can compute with unprecedented precision susceptibilities of the order parameter. In O($N$) Gross-Neveu transitions, the anomalous dimension of the bosonic mode grows as a function of $N$ such that in the large-$N$ limit it is of particular importance to consider susceptibilities rather than equal-time correlations so as to minimize contributions from the background. For the $N=3$ case, we obtain $1/\ensuremath{\nu}=1.11(4), {\ensuremath{\eta}}_{\ensuremath{\phi}}=0.80(9)$, and ${\ensuremath{\eta}}_{\ensuremath{\psi}}=0.29(2)$, respectively, for the correlation length exponent, and the bosonic and fermionic anomalous dimensions.