Algebraic Bethe ansatz for Q-operators: The Heisenberg spin chain

TL;DR

This paper applies the algebraic Bethe ansatz to diagonalize Q-operators in the Heisenberg spin chain, establishing their eigenvalues as Baxter's Q-functions through explicit commutation relations.

Contribution

It provides a direct algebraic proof that Q-operators act diagonally on Bethe vectors and their eigenvalues are Baxter's Q-functions for the rational homogeneous sl(2) spin chain.

Findings

Q-operators act diagonally on Bethe vectors when Bethe equations are satisfied

Eigenvalues of Q-operators are given by Baxter's Q-functions

Derived fundamental commutation relations from the Yang-Baxter equation

Abstract

We diagonalize Q-operators for rational homogeneous sl(2)-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang-Baxter equation we demonstrate that the Q-operators act diagonally on the Bethe vectors if the Bethe equations are satisfied. In this way we provide a direct proof that the eigenvalues of the Q-operators studied here are given by Baxter's Q-functions.