On the second reference state and complete eigenstates of the open XXZ chain

TL;DR

This paper investigates the second reference state of the open XXZ spin chain with non-diagonal boundaries, linking it to the Bethe Ansatz and Gaudin models, thereby advancing understanding of eigenstates in integrable systems.

Contribution

It identifies the second reference state and demonstrates its role in deriving complete eigenstates for related models, extending Bethe Ansatz methods.

Findings

Bethe states yield the second set of eigenvalues for the open XXZ chain.

In the quasi-classical limit, Bethe states form complete eigenstates of the Gaudin model.

The work connects Bethe Ansatz solutions with the structure of eigenstates in integrable models.

Abstract

The second reference state of the open XXZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz. In the quasi-classical limit, two sets of Bethe states give the complete eigenstates of the associated Gaudin model.