Bethe Ansatz solution of the small polaron with nondiagonal boundary terms

TL;DR

This paper solves the small polaron model with non-diagonal boundary conditions using integrability techniques, deriving eigenvalues, Bethe Ansatz equations, and eigenstates, including the vacuum state in special cases.

Contribution

It introduces a Bethe Ansatz solution for the small polaron with generic boundary terms, extending previous diagonal boundary solutions to non-diagonal cases.

Findings

Eigenvalues of the model are obtained.

Bethe Ansatz equations for generic boundary conditions are derived.

Explicit eigenstate corresponding to the Fock vacuum is computed.

Abstract

The small polaron with generic, nondiagonal boundary terms is investigated within the framework of quantum integrability. The fusion hierarchy of the transfer matrices and its truncation for particular values of the anisotropy parameter are both employed, so that the spectral problem is formulated in terms of a TQ equation. The solution of this equation for generic boundary conditions is based on a deformation of the diagonal case. The eigenvalues of the model are extracted and the corresponding Bethe Ansatz equations are presented. Finally, we comment on the eigenvectors of the model and explicitly compute the eigenstate of the model which evolves into the Fock vacuum when the off-diagonal boundary terms are switched off.