Multi-parameter deformed and nonstandard $Y(gl_M)$ Yangian symmetry in a novel class of spin Calogero-Sutherland models

TL;DR

This paper introduces a new class of spin Calogero-Sutherland models with multi-parameter deformed Yangian symmetry, featuring many-body spin interactions and potential anyon-like permutation representations, along with conserved quantities and exact solutions.

Contribution

It constructs novel spin Calogero-Sutherland models with nonstandard deformed Yangian symmetry and develops methods to find their conserved quantities and exact wave functions.

Findings

Models exhibit multi-parameter deformed Yangian symmetry.

Spin interactions are derived from Yang-Baxter solutions.

Exact wave functions and conserved quantities are constructed.

Abstract

It is well known through a recent work of Bernard, Gaudin, Haldane and Pasquier (BGHP) that the usual spin Calogero-Sutherland (CS) model, containing particles with $M$ internal degrees of freedom, respects the $Y(gl_M)$ Yangian symmetry. By following and suitably modifying the approach of BGHP, in this article we construct a novel class of spin CS models which exhibit multi-parameter deformed or `nonstandard' variants of $Y(gl_M)$ Yangian symmetry. An interesting feature of such CS Hamiltonians is that they contain many-body spin dependent interactions, which can be calculated directly from the associated rational solutions of Yang-Baxter equation. Moreover, these spin dependent interactions often lead to `anyon like' representations of permutation algebra on the combined internal space of all particles. We also find out the general forms of conserved quantities as well as Lax pairs for the above mentioned class of spin CS models, and describe the method of constructing their exact wave functions.