  We study a quantum phase transition from a massless to massive Dirac fermion
phase in a new two-dimensional bipartite lattice model of electrons that is
amenable to sign-free quantum Monte Carlo simulations. Importantly,
interactions in our model are not only invariant under $\SU(2)$ symmetries of
spin and charge like the Hubbard model, but they also preserve an Ising like
electron spin-charge flip symmetry. From unbiased fermion bag Monte Carlo
simulations with up to 2304 sites, we show that the massive fermion phase
spontaneously breaks this Ising symmetry, picking either anti-ferromagnetism or
superconductivity and that the transition at which both orders are
simultaneously quantum critical, belongs to a new "chiral spin-charge
symmetric" universality class. We explain our observations using effective
potential and renormalization group calculations within the framework of a
continuum field theory.
