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In the Hamiltonian picture, free spin-$1/2$ Dirac fermions on a bipartitelattice have an $O(4)$ (spin-charge) symmetry. Here we construct an interactinglattice model with an interaction $V$, which is similar to the Hubbardinteraction but preserves the spin-charge flip symmetry. By tuning the coupling$V$, we show that we can study the phase transition between the masslessfermion phase at small-$V$ and a massive fermion phase at large-$V$. Weconstruct a fermion bag algorithm to study this phase transition and findevidence for it to be second order. Numerical study shows that the universalityclass of the transition is different from the one studied earlier involving theHubbard coupling $U$. Here we obtain some critical exponents using lattices upto $L=48$.

Critical exponents for a spin-charge flip symmetric fixed point in 2+1d with massless Dirac fermions