Topological term in the non-linear σ model of the [formula omitted] spin chains

Abstract

We show that there is a topological (Berry phase) term in the non-linear σ model description of the SO ( 5 ) spin chain. It distinguishes the linear and projective representations of the SO ( 5 ) symmetry group, in exact analogy to the well-known θ-term of the SO ( 3 ) spin chain. The presence of the topological term is due to the fact that π 2 ( SO ( 5 ) SO ( 3 ) × SO ( 2 ) ) = Z . We discuss the implication of our results on the spectra of the SO ( 5 ) spin chain, and connect it with a recent solvable SO ( 5 ) spin model which exhibits valence bond solid ground state and edge degeneracy.