From spinons to magnons in explicit and spontaneously dimerized antiferromagnetic chains

TL;DR

This paper analyzes the excitation spectra of dimerized and frustrated antiferromagnetic chains, showing how magnons emerge from spinons and how their properties depend on dimerization strength, using semiclassical methods on a two-frequency Sine-Gordon model.

Contribution

It provides a detailed semiclassical analysis of magnon and spinon excitations in dimerized antiferromagnetic chains, linking the spectrum to dimerization and frustration effects.

Findings

Magnons are extended excitations with diverging radius at zero dimerization.

Excited states arise from internal magnon oscillations and two-magnon continua.

Magnon formation results from spinon-spinon interactions in weak dimerization regimes.

Abstract

We reconsider the excitation spectra of a dimerized and frustrated antiferromagnetic Heisenberg chain. This model is taken as the simpler example of compiting spontaneous and explicit dimerization relevant for Spin-Peierls compounds. The bosonized theory is a two frequency Sine-Gordon field theory. We analize the excitation spectrum by semiclassical methods. The elementary triplet excitation corresponds to an extended magnon whose radius diverge for vanishing dimerization. The internal oscilations of the magnon give rise to a series of excited state until another magnon is emited and a two magnon continuum is reached. We discuss, for weak dimerization, in which way the magnon forms as a result of a spinon-spinon interaction potential.