Quantum critical behavior in three dimensional lattice Gross-Neveu models

Abstract

We study quantum critical behavior in three dimensional lattice Gross-Neveu models containing two four-component massless Dirac fermions. We focus on two models with $SU(2)$ flavor symmetry and either a ${Z}_{2}$ or a $U(1)$ chiral symmetry. Both models could not be studied earlier due to sign problems. We use the fermion bag approach which is free of sign problems and compute critical exponents at the phase transitions. We estimate $\ensuremath{\nu}=0.83(1)$, $\ensuremath{\eta}=0.62(1)$, ${\ensuremath{\eta}}_{\ensuremath{\psi}}=0.38(1)$ in the ${Z}_{2}$ and $\ensuremath{\nu}=0.849(8)$, $\ensuremath{\eta}=0.633(8)$, ${\ensuremath{\eta}}_{\ensuremath{\psi}}=0.373(3)$ in the $U(1)$ model.