Algebraic Bethe ansatz for the six vertex model with upper triangular $K$-matrices

TL;DR

This paper develops an algebraic Bethe ansatz approach for the six vertex model with upper triangular non-diagonal boundary matrices, addressing the challenge of constructing excited states using an auxiliary transfer matrix.

Contribution

It introduces a method to construct excited states in the algebraic Bethe ansatz for models with upper triangular boundary matrices, expanding the solvable boundary conditions.

Findings

Successful construction of excited states using an auxiliary transfer matrix

Extension of algebraic Bethe ansatz to non-diagonal boundary conditions

Framework applicable to models with upper triangular K-matrices

Abstract

We consider a formulation of the algebraic Bethe ansatz for the six vertex model with non-diagonal open boundaries. Specifically, we study the case where both left and right $K$-matrices have an upper triangular form. We show that the main difficulty entailed by those form of the $K$-matrices is the construction of the excited states. However, it is possible to treat this problem with aid of an auxiliary transfer matrix and by means of a generalized creation operator.