Complementary colors of colorons: The elementary excitations of the Haldane-Shastry modelD. 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 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.
© EDP Sciences 2005