A Q-Operator Identity for the Correlation Functions of the Infinite XXZ Spin-Chain

TL;DR

This paper constructs explicit Q-operators for the finite XXZ spin-chain with various boundary conditions, providing an alternative expression for correlation functions in the infinite lattice model.

Contribution

It introduces a new explicit construction of Q-operators for the XXZ spin-chain, applicable to different regimes and boundary conditions, enhancing the understanding of correlation functions.

Findings

Explicit Q-operator construction for finite XXZ chains.

Alternative expression for trace functions in infinite lattice correlation functions.

Applicability to massless, massive, and root of unity regimes.

Abstract

An explicit construction for Q-operators of the finite XXZ spin-chain with twisted boundary conditions is presented. The massless and the massive regime is considered as well as the root of unity case. It is explained how these results yield an alternative expression for the trace function employed in the description of the correlation functions of the inhomogeneous XXZ model on the infinite lattice by Boos, Jimbo, Miwa, Smirnov and Takeyama(hep-th/0412191).