Baxter Q- operator and functional relations

TL;DR

This paper constructs Baxter Q-operators for $U_q( ilde{sl}_2)$-invariant models using functional relations and explicit calculations, deriving the Baxter equation from fusion relations applicable to various integrable models.

Contribution

It introduces a method to obtain Baxter Q-operators as limits of transfer matrices for models with quantum group symmetry, applicable to a broad class of integrable systems.

Findings

Baxter Q-operators derived from transfer matrices.

Baxter equation obtained from fusion relations.

Method applicable to models like the XXZ spin chain.

Abstract

We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from the explicit calculations. We derive the Baxter equation from the well known fusion relations for the transfer matrices. Our method is valid for an arbitrary integrable model corresponding to the quantum group $U_q(\hat{sl}_2)$ for example for the XXZ- spin chain.