INVESTIGATION OF DIFFERENT CLASSES OF VARIATIONAL FUNCTIONS FOR THE TRIANGULAR AND KAGOME SPIN-1/2 HEISENBERG ANTIFERROMAGNETS

We investigate a class of resonating-valence-bond wave functions on the triangular lattice which interpolate between the square-root 3 x square-root 3 Neel state and a dimer state according to the range of the bands and the similar two classes of resonating-valence-bond wave functions on the kagome lattice constructed from the square-root 3 x square-root 3 and q = 0 Neel states. Numerical calculations show that a square-root 3 x square-root 3 wave function gives for the triangular lattice a variational energy and spin-spin correlations in very good agreement with diagonalization results on 12- and 36-site systems. Rather low variational energies are also obtained with trial functions of the square-root 3 x square-root 3 and q = 0 type for the kagome lattice but spin-spin correlations beyond first neighbors are not in good agreement with diagonalization results on 12- and 36-site systems. For the 12-site system, the spin-spin correlations of the best q = 0 wave function most resemble those of the first excited state. The q = 0 and perhaps the square-root 3 x square-root 3 wave functions may describe excited states close to the ground state in the case of larger systems.