Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains

TL;DR

This paper presents a method to construct Baxter Q-operators for generic sl(N) spin chains by factorizing solutions of the Yang-Baxter equation, leading to new insights into transfer matrix relations.

Contribution

It introduces a novel factorization approach for R-operators and explicitly constructs Baxter Q-operators for sl(N) spin chains, advancing integrable systems theory.

Findings

Factorization of R-operators for sl(N) chains established

Explicit formulas for Baxter Q-operators derived

Transfer matrices expressed as products of Q-operators

Abstract

We develop an approach for constructing the Baxter Q-operators for generic sl(N) spin chains. The key element of our approach is the possibility to represent a solution of the the Yang Baxter equation in the factorized form. We prove that such a representation holds for a generic sl(N) invariant R-operator and find the explicit expression for the factorizing operators. Taking trace of monodromy matrices constructed of the factorizing operators one defines a family of commuting (Baxter) operators on the quantum space of the model. We show that a generic transfer matrix factorizes into the product of N Baxter Q-operators and discuss an application of this representation for a derivation of functional relations for transfer matrices.