Itinerant Antiferromagnetism in an Infinite Linear Chain

Abstract

Overhauser's spin-density-wave state of a general pitch $Q$ is considered for a linear chain with a half-filled band. It is found that $Q=2\mathrm{}{k}_F$ for all values of the coupling constant. Comparison is made with other Hartree-Fock states, and with a recent exact expression for the ground-state energy. The collective modes of the system are calculated numerically, and for large coupling constant they are found to behave as $\omega \mathrm{}\left(q\right)\mathrm{}\sim \left|sin\mathrm{}\right(\mathrm{qa}\left)\right|$.