Antiferromagnetic Spin Waves

Abstract

The ground state of the antiferromagnetic spin-1/2 linear chain is a made up of a linear combination of basis states with exactly half (N/2) the spins reversed. The elementary excitations from the ground state have $N/2 \pm 1$ spins reversed. To calculate the energies of these states, des Cloiseaux and Pearson used a modified version of the same method that Hulthén had used for the ground state energy. The modifications are quite significant and involve some rather different mathematical techniques. These are described in this chapter. The result is not a single branch of excitations as a function of the total wave vector, but rather a continuum of states. The lower boundary of this continuum has a simple sine-wave form, which is similar to that obtained using conventional antiferromagnetic spin-wave theory (covered in a later chapter). We finish this chapter with a discussion of the somewhat unexpected behaviour of the excitation spectrum when an external magnetic field is present.