Abstract
We diagonalize Q-operators for rational homogeneous -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.
Highlights
Integrable spin chains are prominent examples of integrable models
We diagonalized the Q-operators for the XXXs Heisenberg spin chain using the algebraic Bethe ansatz
In doing so we demonstrate that the eigenvalues of the Q-operators are given by Baxters Q-functions
Summary
Integrable spin chains are prominent examples of integrable models. The solution of the Heisenberg XXX 1 spin chain goes back to Bethe [1]. Combined with the algebraic Bethe ansatz, that allows to determine the wave function for models with a suitable reference state, it yields a powerful tool to diagonalize integrable Hamiltonians along with the commuting family of operators, see e.g. Having derived the quantum Wronskian and in particular the QQrelations on the operatorial level it was argued that the eigenvalues of the constructed Qoperators are the Q-functions, see section 3.5 in [9] It was shown in [13] how local charges can be obtained from the Q-operators. We show that the Qoperators act diagonally on the Bethe vectors This pragmatic approach motivates the choice of Lax operators used to construct the Qoperators, avoids the detour of deriving the functional relations from the factorization formulas and provides a transparent derivation of the eigenvalues of the Q-operators along with the corresponding eigenvectors.
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