Investigation of different classes of variational functions for the triangular and kagome-acute spin-1/2 Heisenberg antiferromagnets.

Abstract

We investigate a class of resonating-valence-bond wave functions on the triangular lattice which interpolate between the \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 N\'eel state and a dimer state according to the range of the bonds and the similar two classes of resonating-valence-bond wave functions on the kagome$aa\char22{} lattice constructed from the \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 and q=0 Ne\'el states. Numerical calculations show that a \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 wave function gives for the triangular lattice a variational energy and spin-spin correlations in very good agreement with diagonalization results on 12- and 36-site systems. Rather low variational energies are also obtained with trial functions of the \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 and q=0 type for the kagome$aa\char22{} 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 \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 wave functions may describe excited states close to the ground state in the case of larger systems.