Variational Monte-Carlo studies of Gossamer Superconductivity

We use a partially Gutzwiller projected BCS d-wave wavefunction with an antiferromagentic weighting factor to study the ground state phase diagram of a half filled Hubbard-Heisenberg model in a square lattice with nearest neighbor hopping $t$ and a diagonal hopping $t^{\mathrm{\prime }}$. The calculations are carried out by using variational Monte Carlo method which treats the Gutzwiller projection explicitly. At large on-site Coulomb interaction $U$, the ground state is antiferromagnetic. As $U$ decreases, the ground state becomes superconducting and eventually metallic. The phase diagram is obtained by extensive calculations. As compared to the strong effect of $U\mathrm{/}t$, the phase boundaries turn out to be less sensitive to $t^{\mathrm{\prime }}\mathrm{/}t$. The result is consistent with the phase diagram in layered organic conductors, and is compared to the earlier mean field result based on the Gutzwiller approximation.