SU(\nu) Generalization of Twisted Haldane-Shastry Model

TL;DR

This paper explores the SU(ν) generalization of the twisted Haldane-Shastry model, deriving exact wavefunctions and analyzing spectral flow, revealing a period related to exclusion statistics.

Contribution

It provides exact Jastrow wavefunctions for all rational twist angles and links spectral flow period to exclusion statistics in the SU(ν) model.

Findings

Exact wavefunctions for rational twist angles

Spectral flow period equals ν

Spectral flow depends on exclusion statistics

Abstract

The SU($\nu$) generalized Haldane-Shastry spin chain with $1/r^2$ interaction is studied with twisted boundary conditions. The exact wavefunctions of Jastrow type are obtained for every rational value of the twist angle in unit of $2\pi$. The spectral flow of the ground state is then discussed as a function of the twist angle. By resorting to the motif picture in the Bethe ansatz method, we show that the period of the spectral flow is $\nu$, which is determined by the statistical interaction in exclusion statistics.