Exact Dynamics of the SU(K) Haldane-Shastry Model

Abstract

The dynamical structure factor $S(q,\omega )$ of the SU(K) (K=2,3,4) Haldane-Shastry model is derived exactly at zero temperature for arbitrary size of the system. The result is interpreted in terms of free quasi-particles which are generalization of spinons in the SU(2) case; the excited states relevant to $S(q,\omega )$ consist of K quasi-particles each of which is characterized by a set of K-1 quantum numbers. Near the boundaries of the region where $S(q,\omega )$ is nonzero, $S(q,\omega )$ shows the power-law singularity. It is found that the divergent singularity occurs only in the lowest edges starting from $(q,\omega )=(0,0)$ toward positive and negative q. The analytic result is checked numerically for finite systems via exact diagonalization and recursion methods.

35 pages, 3 figures, youngtab.sty (version 1.1)

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• Phase diagram of a 1 dimensional spin-orbital model
• Exact dynamical structure factor of the degenerate Haldane-Shastry model
• Crossover Phenomena in the One-Dimensional SU(4) Spin-Orbit Model under Magnetic Fields
• Exclusion statistics in conformal field theory and the UCPF for WZW models
• Exact Charge Dynamics in the Supersymmetric t-J Model with Inverse-Square Interaction
• Dynamical correlation functions of the spin Calogero-Sutherland model

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• Finite temperature structure factor in the Haldane-Shastry spin chain
• Dynamical Properties of the 1/r^2-Type Supersymmetric t-J Model in a Magnetic Field: Manifestation of Spin-Charge Separation
• Derivation of Green's Function of Spin Calogero-Sutherland Model by Uglov's Method
• The dynamical structure factor of the SU(3) Heisenberg chain: The variational Monte Carlo approach