A note on inverse-square exchange models

TL;DR

This paper explores the diagonalization of the su(1|1) symmetric Haldane-Shastry spin chain and extends the transformation to the su(2) model, revealing simplified Hamiltonian expressions and Yangian symmetry generators.

Contribution

It introduces a linear transformation approach to diagonalize the su(1|1) model and simplifies the su(2) model's Hamiltonian and symmetry generators.

Findings

Diagonalization of su(1|1) Haldane-Shastry model achieved.

Simplified expressions for su(2) Hamiltonian and Yangian generators.

Extension of transformation method to related models.

Abstract

The su(1$|$1) symmetric version of the Haldane-Shastry spin chain is diagonalized by means of a linear transformation. The same transformation applied to the original su(2) model yields simple expressions for the Hamiltonian and the generators of the Yangian symmetry of the model in terms of spin wave operators.