Non-linear Field Theory of a Frustrated Heisenberg Spin Chain

TL;DR

This paper develops a continuum field theory for the frustrated Heisenberg spin chain, revealing a disordered phase at long distances with massive excitations, applicable to both integer and half-integer spins.

Contribution

It introduces a non-linear field theory for the Majumdar-Ghosh model in the large-$S$ limit, showing the absence of topological terms and analyzing its flow towards a disordered phase.

Findings

Flow towards strong coupling at long distances

All excitations are massive in the large-$N$ limit

No topological term distinguishes integer and half-integer spins

Abstract

We derive a continuum field theory for the Majumdar-Ghosh model in the large-$S$ limit, where the field takes values in the manifold of the $SO(3)$ group. 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 $\beta -$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. (Three figures not included)