Close Relation between Localized-Electron Magnetism and the Paramagnetic Wave Function of Completely Itinerant Electrons

What is commonly called the Gutzwiller wave function $\psi$, an approximate ground state of the single-band Hubbard Hamiltonian, is considered here for $N$-site $N$-electron rings, when the number $D$ of doubly occupied sites is small ($N=6, 10, 14, 18$). For $D\to 0$ spin correlations in $\psi$ surprisingly close to the exact values at zero bandwidth are found (i.e., those of the antiferromagnetic Heisenberg-model ground state). But the energy is grossly in error. A simple modification of $\psi$ reproduces the exact energy with remarkable accuracy.