We study ground state degeneracy and spin-wave excitations in a 1D version of a Kagome antiferromagnet -- a Heisenberg antiferromagnet on a Kagome stripe. We show that for nearest-neighbor interaction, the classical ground state is infinitely degenerate. For any spin configuration from the degenerate set, the classical spin-wave spectrum contains, in addition to Goldstone modes, a branch of zero energy excitations, and a zero mode in another branch. We demonstrate that the interactions beyond nearest neighbors lift the degeneracy, eliminate a zero mode, and give a finite dispersion to formerly zero-energy branch, leaving only Goldstone modes as zero-energy excitations.
@article{arxiv.0708.1272,
title = {Spin-wave spectra of a kagome stripe},
author = {A. Donkov and A. V. Chubukov},
journal= {arXiv preprint arXiv:0708.1272},
year = {2009}
}