Q-operators for higher spin eight vertex models with an even number of sites

TL;DR

This paper constructs Q-operators for higher spin eight vertex models linked to the Sklyanin algebra and proves a sum rule for Bethe roots, extending Baxter's foundational work.

Contribution

It introduces a generalized Q-operator framework for higher spin models and establishes a key sum rule for Bethe roots, advancing integrable systems theory.

Findings

Construction of Q-operators for higher spin models

Proof of the sum rule for Bethe roots

Extension of Baxter's 1973 methods

Abstract

We construct the Q-operator for generalised eight vertex models associated to higher spin representations of the Sklyanin algebra, following Baxter's 1973 paper. As an application, we prove the sum rule for the Bethe roots.