A Bipartite Spin 1/2 Heisenberg-Model With A Gap to Excitations

We consider the nearest neighbour quantum mechanical Heisenberg model acting on two simple one-dimensional chains of spin 1/2 atoms. By showing that these models can be mapped onto a chain of spin 1 composites, we deduce that the spectrum has a gap, provided that the spin 1 chain has a gap. This result is in contrast to that found for the chain of spin 1/2 atoms and suggests that a distinction between integer and half-integer spins is restricted to the linear chain. We present a simple interpretation for the spin correlations of the low energy excitations and give new numerical evidence for a gap in the spectrum of the spin 1 chain. The lowest lying spin 1/2 chain excitation is a domain wall, but the lowest lying spin 1 chain excitation has previously been suggested to have spin-wave properties, we test this hypothesis numerically.