Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields

TL;DR

This paper constructs Bethe eigenstates for the XXZ spin-1/2 chain with arbitrary boundary fields using an inhomogeneous T-Q relation and gauge transformations, proving their eigenstate property under Bethe Ansatz equations.

Contribution

It introduces a method to explicitly construct Bethe states for the XXZ chain with arbitrary boundary conditions using the off-diagonal Bethe Ansatz and gauge transformations.

Findings

Bethe states are explicitly constructed for arbitrary boundary fields.

Proven that these states are eigenstates of the transfer matrix.

Established the conditions under which the Bethe states satisfy the eigenvalue equations.

Abstract

Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin-1/2 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge transformations, proper generators and reference state for constructing Bethe vectors can be obtained respectively. Given an inhomogeneous T-Q relation for an eigenvalue, it is proven that the resulting Bethe state is an eigenstate of the transfer matrix, provided that the parameters of the generators satisfy the associated Bethe Ansatz equations.