Non-linear field theory of a frustrated Heisenberg spin chain

Abstract

We derive a continuum field theory for the Majumdar-Ghosh model in the large-S limit. The field takes values in the manifold of the group SO(3) and the field theory is not Lorentz-invariant. No topological term is induced in the action and the cases for integer spin and half-integer spin appear to be indistinguishable. A one-loop β-function calculation indicates that the theory flows towards a strong coupling (disordered) phase at long distances. This is verified in the large-N limit, where all excitations are shown to be massive.