Exact ground states for a class of antiferromagnetic Heisenberg models with short-range interactions

A special class of Heisenberg spin Hamiltonians with short-range antiferromagnetically signed interactions is described. It is demonstrated via a simple group-theoretic argument that the ground states to many of these Hamiltonians are Kekule states, involving singlet spin-pairing between nearest-neighbour pairs of sites. A number of examples are given and previous related work is indicated. In addition to standard applications to exchange-coupled atomic ions, the relevance of this work for the simple valence-bond model of conjugated pi -electron networks is mentioned.