Algebraic representation of correlation functions in integrable spin chains

TL;DR

This paper reviews an algebraic approach to calculating correlation functions in integrable spin chains, focusing on the XXZ model and extending to homogeneous chains, quantum group invariance, and the XYZ chain.

Contribution

It presents a unified algebraic framework for correlation functions applicable to various integrable spin chains, including homogeneous and quantum group invariant cases.

Findings

Algebraic formulas effectively describe correlation functions in the XXZ chain.

Extension of methods to homogeneous chains improves practical applicability.

Generalization to the XYZ chain broadens the scope of algebraic representations.

Abstract

Taking the XXZ chain as the main example, we give a review of an algebraic representation of correlation functions in integrable spin chains obtained recently. We rewrite the previous formulas in a form which works equally well for the physically interesting homogeneous chains. We discuss also the case of quantum group invariant operators and generalization to the XYZ chain.