Physics of the Ideal Semion Gas: Spinons and Quantum Symmetries of the Integrable Haldane-Shastry Spin Chain

TL;DR

This paper reviews the physics of the Haldane-Shastry spin chain, highlighting its quantum group symmetry, fractional statistics of spinons, and recent results on dynamical correlations, extending to SU(n) and Calogero-Sutherland models.

Contribution

It provides a comprehensive review of the Haldane-Shastry model's quantum symmetries and fractional statistics, including new conjectures on dynamical correlations for generalized models.

Findings

Analysis of the Yangian quantum group structure

Recent results on dynamical correlation functions

Conjectured extensions to SU(n) and Calogero-Sutherland models

Abstract

Various aspects of the Haldane-Shastry spin chain with 1/r^2 exchange, and its various generalizations, are reviewed, with emphasis on its Yangian quantum group structure, and the interpretation of the model as the generalization of an ideal gas (of ``spinons'') to the case of fractional statistics. Some recent results on its dynamical correlation function are discussed, and conjectured extensions of these remarkably simple results to the $SU(n)$ model, and to the related Calogero-Sutherland model with integer coupling constant, are presented. (Talk presented at the 16th. Taniguchi Symposium, Kashikojima, Japan, October 26-29, 1993)