HEISENBERG-ANTIFERROMAGNET ON TRIANGULATED TREES

We study the spin-1/2 antiferromagnetic Heisenberg Hamiltonian with nearest-neighbour pair interaction on some graphs with an odd number of vertices, called triangulated trees. The model has valence bond ground states in which there is a localized spinon (1/2 spin) on some site. The space of ground states for a tree of L triangles is 2(L + 1) dimensional. In the limit of infinite volume we find an infinity of pure ground states. To any (infinite) branch of the tree there belongs a spin-Peierls ground state without spinon. There is an infinite family of equivalent pure ground states differing only locally, in the position of the spinon. In any finite-volume ground state the pair correlations decay exponentially. For the chain of triangles we show the existence of a gap in the energy spectrum above the ground state.