Many-spinon states and the secret significance of Young tableaux

TL;DR

This paper reveals a precise correspondence between Young tableaux, which classify spin representations, and the eigenstates of the Haldane-Shastry model, linking spin states to spinon momenta.

Contribution

It establishes a one-to-one mapping between Young tableaux and the exact eigenstates of the Haldane-Shastry model, connecting representation theory with physical states.

Findings

Young tableaux classify total spin representations.

Eigenstates correspond to specific Young tableaux.

Spinon momenta are linked to Young tableau structures.

Abstract

We establish a one-to-one correspondence between the Young tableaux classifying the total spin representations of N spins and the exact eigenstates of the the Haldane-Shastry model for a chain with N sites classified by the total spins and the fractionally spaced single-particle momenta of the spinons.