Quantum criticality in SU(3) and SU(4) anti-ferromagnets

We study the quantum phase transition out of the Neel state in SU(3) and SU(4) generalizations of the Heisenberg anti-ferromagnet with a sign problem free four spin coupling (so-called JQ model), by extensive quantum Monte Carlo simulations. We present evidence that the SU(3) and SU(4) order parameters and the SU(3) and SU(4) stiffness' go to zero continuously without any evidence for a first order transition. However, we find considerable deviations from simple scaling laws for the stiffness even in the largest system sizes studied. We interpret these as arising from multiplicative scaling terms in these quantities which affect the leading behavior, i.e., they will persist in the thermodynamic limit unlike the conventional additive corrections from irrelevant operators. We conjecture that these multiplicative terms arise from dangerously irrelevant operators whose contributions to the quantities of interest are non-analytic.