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

We diagonalize Q-operators for rational homogeneous $sl\left(2\right)$-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. (paper)