Volume 71, Number 6, September 2005
|Page(s)||987 - 993|
|Section||Condensed matter: electronic structure, electrical, magnetic, and optical properties|
|Published online||10 August 2005|
Complementary colors of colorons: The elementary excitations of the Haldane-Shastry model
Institut für Theorie der Kondensierten Materie, Universität Karlsruhe Postfach 6980, 76128 Karlsruhe, Germany
Accepted: 11 July 2005
We propose two possible trial wave functions for the elementary excitations of the Haldane-Shastry model, but then argue on very general grounds that only one or the other can be a valid excitation. We then prove explicitly that the trial wave function describing a coloron excitation which transforms according to representation under rotations if the spins of the original model transform according to representation 3, is exact. If a basis for the spins on the chain is spanned by the colors blue, red, and green, a basis for the coloron excitations is hence given by the complementary colors yellow, cyan, and magenta. We derive the dispersion and show that colorons exist only in one-third of the Brillouin zone. We further obtain the exclusion statistics among polarized colorons and discuss the generalization to .
PACS: 75.10.Pq – Spin chain models / 02.30.Ik – Integrable systems / 75.10.Jm – Quantized spin models
© EDP Sciences, 2005
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