Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin

TL;DR

This paper constructs and diagonalizes Q-operators for the open XXX Heisenberg chain with arbitrary spin using algebraic Bethe ansatz, providing explicit eigenvalues in terms of Bethe roots.

Contribution

It introduces a method to construct and diagonalize Q-operators for the open XXX chain with arbitrary spin, extending previous algebraic Bethe ansatz techniques.

Findings

Eigenvalues expressed in terms of Bethe roots

Unwanted terms vanish when Bethe equations are satisfied

Framework applicable to arbitrary spin chains

Abstract

In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in the framework of the quantum inverse scattering method. Following the algebraic Bethe ansatz we diagonalise the introduced Q-operators using the fundamental commutation relations. By acting on Bethe off-shell states and explicitly evaluating the trace in the auxiliary space we compute the eigenvalues of the Q-operators in terms of Bethe roots and show that the unwanted terms vanish if the Bethe equations are satisfied.