Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions

TL;DR

This paper presents an exact solution for the XXX spin chain with arbitrary boundary conditions using the off-diagonal Bethe ansatz, expanding the analytical tools for integrable models with complex boundaries.

Contribution

It introduces a novel application of the off-diagonal Bethe ansatz to solve the XXX spin chain with arbitrary boundary fields, deriving the transfer matrix eigenvalues and Bethe equations.

Findings

Exact diagonalization of the XXX spin chain with arbitrary boundaries.

Derivation of the T-Q relation and Bethe ansatz equations.

Extension of Bethe ansatz methods to more general boundary conditions.

Abstract

With the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the $XXX$ spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated $T-Q$ relation and the Bethe ansatz equations are derived.