  Competing unconventional superconductivity and antiferromagnetism widely
exist in several strongly correlated quantum materials whose direct simulation
generally suffers from fermion sign problem. Here we report unbiased Quantum
Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with
same onsite symmetries as the standard Hubbard model on a 2D square lattice.
Using QMC, supplemented with mean-field and continuum field-theory arguments,
we find that it hosts three distinct phases: a nodal d-wave phase, an
antiferromagnet, and an intervening phase which hosts coexisting
antiferromagnetism and nodeless d-wave superconductivity. The transition from
the coexisting phase to the antiferromagnet is described by the 2+1-D XY
universality class, while the one from the coexisting phase to the nodal d-wave
phase is described by the Heisenberg-Gross-Neveu theory. The topology of our
phase diagram resembles that of layered organic materials which host pressure
tuned Mott transition from antiferromagnet to unconventional superconductor at
half-filling.
