Baxter Q-operators of the XXZ chain and R-matrix factorization

TL;DR

This paper constructs Baxter Q-operators for the XXZ chain using R-matrix factorizations, providing explicit formulas and insights into their properties, advancing understanding of integrable quantum models.

Contribution

It introduces a novel method to explicitly construct Baxter Q-operators via R-matrix factorization, enhancing analytical tools for integrable systems.

Findings

Explicit expressions for Baxter Q-operators derived

Factorization of R-matrices into simpler operators demonstrated

Foundations laid for further analysis of Q-operator properties

Abstract

We construct Baxter operators as generalized transfer matrices being traces of products of generic $R$ matrices. The latter are shown to factorize into simpler operators allowing for explicit expressions in terms of functions of a Weyl pair of basic operators. These explicit expressions are the basis for explicit expression for Baxter Q-operators and for investigating their properties.