Effects of flavor-symmetry violation from staggered fermion lattice simulations of graphene

We analyze the effects of flavor splitting from staggered fermion lattice simulations of a low-energy effective theory for graphene. Both the unimproved action and the tadpole-improved action with a Naik term show significant flavor-symmetry breaking in the spectrum of the Dirac operator. Note that this is true even in the vicinity of the second-order phase transition point where it has been argued that the flavor-symmetry breaking should be small due to the continuum limit being approached. We show that at weaker couplings the flavor splitting is drastically reduced by stout link smearing, while this mechanism is ineffective at the stronger couplings relevant to suspended graphene. We also measure the average plaquette and describe how it calls for a reinterpretation of previous lattice Monte Carlo simulation results, due to tadpole improvement. After taking into account these effects, we conclude that previous lattice simulations are possibly indicative of an insulating phase, although the effective number of light flavors could be effectively less than two due to the flavor-splitting effects. If that is true, then simulations with truly chiral fermions (such as overlap fermions) are needed in order to settle the question.