Competing nodal d-wave superconductivity and antiferromagnetism: a Quantum Monte Carlo study*

Unconventional superconductors such as cuprates often host competing nodal superconductivity and antiferromagnetism. These systems are typically modeled as a repulsive Hubbard model whose unbiased simulation suffers from the fermion sign-problem at any non-zero doping. Here we will exploit the fact that neither of these phases, the nodal d-wave superconductor or the antiferromagnet, require any doping for their existence, and construct a sign-problem-free repulsive Hubbard model with an additional bosonic field which hosts both of these phases. Using Quantum Monte Carlo (QMC) simulations, supplemented with mean-field theory 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 chiral Gross-Neveu-Heisenberg theory.