Multiplicity in Supersymmetric Spin Chains

TL;DR

This paper introduces a method to generate new integrable supersymmetric spin chains by replacing single states with collections, and solves these models using the nested algebraic Bethe ansatz.

Contribution

It presents a simple procedure to construct new integrable models from existing ones and applies the nested algebraic Bethe ansatz to solve supersymmetric cases.

Findings

New integrable supersymmetric spin chains constructed

Solution of these chains via nested algebraic Bethe ansatz

Extension of the method to bosonic and supersymmetric models

Abstract

We discuss a simple procedure for obtaining new integrable spin chains from old by replacing each single state of the original model by some collection of states. This works whenever the Lax matrix of the chain has a certain form. The simplest example is the su(n) XX model. We apply the techniques of the nested algebraic Bethe ansatz to solve such systems, in the bosonic and supersymmetric cases.