Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields

TL;DR

This paper develops an off-diagonal Bethe ansatz method to solve anisotropic spin-1/2 chains with arbitrary boundary fields, deriving transfer matrix identities and Bethe ansatz equations for XXZ and XYZ models.

Contribution

It introduces a novel off-diagonal Bethe ansatz approach for boundary field problems in spin chains, extending solvability to more general boundary conditions.

Findings

Derived operator product identities for transfer matrices.

Established extended T-Q ansatzs for XXZ and XYZ models.

Formulated Bethe ansatz equations for arbitrary boundary fields.

Abstract

The anisotropic spin-1/2 chains with arbitrary boundary fields are diagonalized with the off-diagonal Bethe ansatz method. Based on the properties of the R-matrix and the K-matrices, an operator product identity of the transfer matrix is constructed at some special points of the spectral parameter. Combining with the asymptotic behavior (for XXZ case) or the quasi-periodicity properties (for XYZ case) of the transfer matrix, the extended T-Q ansatzs and the corresponding Bethe ansatz equations are derived.