Effective spin-wave action for ordered Heisenberg antiferromagnets in a magnetic field

TL;DR

This paper derives a modified effective action for spin-waves in ordered quantum antiferromagnets under magnetic fields, revealing discrepancies with traditional models and highlighting the importance of additional interactions.

Contribution

It introduces a new effective action that includes a quartic interaction term, improving the description of spin-waves in magnetic fields beyond the standard nonlinear sigma model.

Findings

Discrepancy between traditional sigma model predictions and spin-wave theory.

Derivation of a modified effective action with an additional quartic term.

Relevance of the vertex in the renormalization group sense below three dimensions.

Abstract

We derive the effective long-wavelength Euclidean action for the antiferromagnetic spin-waves of ordered quantum antiferromagnets subject to a uniform magnetic field. We point out that the magnetic field dependence of the spin-wave dispersion predicted by the usual O(3)-quantum nonlinear sigma model disagrees with spin-wave theory. We argue that the nonlinear sigma model does not take into account all relevant spin-wave interactions and derive a modified effective action for the long-wavelength spin-waves which contains an additional quartic interaction. At zero temperature the corresponding vertex is relevant in the renormalization group sense below three dimensions.