Magnetic excitation spectrum of dimerized antiferromagnetic chains

TL;DR

This paper investigates the magnetic excitation spectrum of an antiferromagnetic S=1/2 chain with alternating couplings, revealing magnons, continua, and bound states consistent with experimental data.

Contribution

It provides a theoretical analysis of the excitation spectrum in dimerized antiferromagnetic chains, including predictions of bound states and continuum behavior.

Findings

Magnons and continua with square root edges identified

Spectral density of continua calculated

Bound states of two magnons predicted

Abstract

Motivated by recent measurements on CuGeO$_3$ the spectrum of magnetic excitations of an antiferromagnetic $S=\frac{1}{2}$ chain with alternating coupling strength is investigated. Wave vector dependent magnons and a continuum with square root behavior at the band edges are found. The spectral density of the continua is calculated. Spin rotation symmetry fixes the gap of the continuum to be twice the elementary magnon gap. This is in excellent agreement with experimental results. In addition, the existence of bound states of two magnons is predicted: below the continuum a singlet and a triplet, above the continuum an ``anti-bound'' quintuplet. The results are based on field theoretic arguments, RPA calculations, and consideration of the limit of strong alternation.