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

TL;DR

This paper derives the exact zero-temperature dynamical structure factor for the SU(K) Haldane-Shastry model, revealing power-law singularities and interpreting excitations as generalized spinons across different K values.

Contribution

It provides the first exact analytical expression for $S(q,omega)$ in the SU(K) Haldane-Shastry model for arbitrary system size, extending understanding of quasi-particle excitations.

Findings

Power-law singularities occur at the edges of the nonzero region of $S(q,omega)$.

Divergent singularities are confined to the lowest edges starting from (0,0).

Numerical checks confirm the analytical results for finite systems.

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.