New spin generalisation for long range interaction models

TL;DR

This paper introduces new long-range interaction models in spin systems based on Lie algebra symmetries, revealing specific coupling conditions for their symmetry algebras to emerge.

Contribution

It identifies novel interactions in Calogero and Sutherland models and determines their symmetry algebras, which depend on specific coupling constants.

Findings

Symmetry algebras are half-loop algebras for Calogero models.

Symmetry algebras are Yangians for other models.

Symmetries occur only at specific coupling values.

Abstract

We study new interactions between degrees of freedom for Calogero, Sutherland and confined Calogero spin models. These interactions are encoded by the generators of the Lie algebra so(N) or sp(N). We find the symmetry algebras of these new models: the half-loop algebra based on so(N) or sp(N) for the Calogero models and the Yangian of so(N) or sp(N) for the two types of other models. Surprisingly, these symmetry occur only for a specific value of the coupling constant.