Semi-classical description of the frustrated antiferromagnetic chain

TL;DR

This paper maps the frustrated antiferromagnetic chain onto a nonlinear sigma model, revealing a disordered phase with a doubly degenerate spin-1 excitation branch, supported by exact diagonalizations.

Contribution

It provides a semi-classical continuum description of the frustrated antiferromagnetic chain and predicts a doubly degenerate spin-1 branch, supported by numerical evidence.

Findings

Disordered phase with a gap in the excitation spectrum

Doubly degenerate spin-1 branch at all orders in 1/N

Support from exact diagonalizations

Abstract

The antiferromagnetic Heisenberg model on a chain with nearest and next nearest neighbor couplings is mapped onto the $SO(3)$ nonlinear sigma model in the continuum limit. In one spatial dimension this model is always in its disordered phase and a gap opens to excited states. The latter form a doubly degenerate spin-1 branch at all orders in $1/N$. We argue that this feature should be present in the spin-1 Heisenberg model itself. Exact diagonalizations are used to support this claim. The inapplicability of this model to half-integer spin chains is discussed.