The Spin 1/2 Heisenberg-Model and the Railroad Trestle Geometry

We study the spin 1/2 Heisenberg model on the 'Railroad Trestle' geometry of two lines of close packed atoms. Our motivation is to try to establish a link between triangular geometries and the Haldane gap. The classical limit of the model involves incommensurate spiralling, but there is a collinear state nearby in energy. We believe that quantum fluctuations stabilize the symmetry associated with the collinear state. We give numerical evidence to suggest that the state stabilized has a spontaneously broken symmetry with similar short range correlations to those found in the spin 1 chain, together with a gap to excitations.