One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains

TL;DR

This paper introduces a new class of supersymmetric Haldane-Shastry-like spin chains invariant under Yangian symmetry, linking their partition functions to one-dimensional vertex models and revealing a boson-fermion duality.

Contribution

It defines a novel class of Yangian invariant spin chains and establishes their equivalence to vertex models, also uncovering a boson-fermion duality in their partition functions.

Findings

Partition functions expressed via super Schur polynomials.

Equivalence between spin chains and vertex models.

Boson-fermion duality relation established.

Abstract

We define a class of $Y(sl_{(m|n)})$ Yangian invariant Haldane-Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials. Using some properties of the super Schur polynomials, we show that the partition functions of this class of spin chains are equivalent to the partition functions of a class of one-dimensional vertex models with appropriately defined energy functions. We also establish a boson-fermion duality relation for the partition functions of this class of supersymmetric HS like spin chains by using their correspondence with one-dimensional vertex models.