Projected Wave Functions and High Temperature Superconductivity

We study the Hubbard model with parameters relevant to cuprates using variational Monte Carlo for projected $d$-wave states. For doping $0<x\lesssim 0.35$ we obtain a superconductor whose order parameter $\Phi \left(x\right)$ tracks the observed nonmonotonic $T_c\left(x\right)$. The variational parameter ${\Delta }_{\mathrm{var}}\left(x\right)$ scales with the $(\pi ,0\mathrm{})$ “hump” and $T^{*}$ seen in photoemission. Projection leads to incoherence in the spectral function and from the singular behavior of its moments we obtain the nodal quasiparticle weight $Z\sim x$ though the Fermi velocity remains finite as $x\to 0$. The Drude weight $D_{\mathrm{low}}$ and superfluid density are consistent with experiment and $D_{\mathrm{low}}\sim Z$.