Excitation Spectra of Linear Magnetic Chains

The restrictions on the excitation spectra of infinite linear magnetic chains due to the invariances of the Hamiltonian under time reversal and spin rotation have been studied by making use of the equivalence of a linear magnetic chain and a one-dimensional assembly of interacting Fermi particles. In particular, the spin-wave spectrum of an infinite antiferromagnetic chain is found to have a double periodicity of $\pi$ in the wave vector, in agreement with the numerical result of des Cloizeaux and Pearson.