Izergin-Korepin analysis on the wavefunctions of the $U_q(sl_2)$ six-vertex model with reflecting end

TL;DR

This paper extends Izergin-Korepin analysis to wavefunctions of the $U_q(sl_2)$ six-vertex model with reflecting boundaries, deriving symmetric functions and algebraic identities, and comparing with Bethe ansatz solutions.

Contribution

It introduces a novel extension of Izergin-Korepin analysis to reflecting boundary conditions, providing explicit symmetric functions and algebraic identities for the wavefunctions.

Findings

Derived explicit symmetric functions for wavefunctions with reflecting boundaries.

Established algebraic identities by combining symmetric functions with determinant formulas.

Compared symmetric functions with Bethe ansatz wavefunctions for the open XXZ chain.

Abstract

We extend the recently developed Izergin-Korepin analysis on the wavefunctions of the $U_q(sl_2)$ six-vertex model to the reflecting boundary conditions. Based on the Izergin-Korepin analysis, we determine the exact forms of the symmetric functions which represent the wavefunctions and its dual. Comparison of the symmetric functions with the coordinate Bethe ansatz wavefunctions for the open XXZ chain by Alcaraz-Barber-Batchelor-Baxter-Quispel is also made. As an application, we derive algebraic identities for the symmetric functions by combining the results with the determinant formula of the domain wall boundary partition function of the six-vertex model with reflecting end.