Many-spinon states and representations of Yangians in the SU(n) Haldane--Shastry model

TL;DR

This paper explores the connection between Yangian algebra representations and fractional statistics of spinons in the SU(n) Haldane--Shastry model, revealing how the Yangian structure underpins the spinon Hilbert space.

Contribution

It demonstrates the deep relationship between Yangian representations and spinon fractional statistics, and constructs the spinon Hilbert space from Yangian fundamental representations.

Findings

Yangian representations relate to spinon fractional statistics

Constructed spinon Hilbert space from Yangian tensor products

Revealed the algebraic structure underlying the model

Abstract

We study the relation of Yangians and spinons in the SU(n) Haldane--Shastry model. The representation theory of the Yangian is shown to be intimately related to the fractional statistics of the spinons. We construct the spinon Hilbert space from tensor products of the fundamental representations of the Yangian.