Exact Jastrow-Gutzwiller resonating-valence-bond ground state of the spin-(1/2 antiferromagnetic Heisenberg chain with 1/r2exchange

A set of Jastrow wave functions comprises exact eigenstates of a family of S= $\frac{1}{2}$ antiferromagnetic chains with ${\mathrm{r}}^{\mathrm{-}2}$ exchange. The ground state of the isotropic model is in this set, and is identical to the U→∞ limit of the Gutzwiller wave function, also identified as Anderson’s ‘‘resonating-valence-bond’’ state. The full set of energy levels of this model is obtained; the spectrum exhibits remarkable ‘‘supermultiplet’’ degeneracies suggesting the existence of a hidden continuous symmetry.