Europhys. Lett.
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
Europhys. Lett., 71 (6), pp. 987-993 (2005)
DOI: 10.1209/epl/i2005-10168-1

Complementary colors of colorons: The elementary excitations of the $\mth{SU(3)}$ Haldane-Shastry model

D. Schuricht and M. Greiter

Institut für Theorie der Kondensierten Materie, Universität Karlsruhe Postfach 6980, 76128 Karlsruhe, Germany

received 9 May 2005; accepted in final form 11 July 2005
published online 10 August 2005

We propose two possible trial wave functions for the elementary excitations of the SU(3) 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 $\bar{3}$ under SU(3) 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 SU(n).

75.10.Pq - Spin chain models.
02.30.Ik - Integrable systems.
75.10.Jm - Quantized spin models.

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