Exact results for the six-vertex model with domain wall boundary conditions and a partially reflecting end

TL;DR

This paper derives exact formulas for the partition function of the trigonometric six-vertex model with domain wall boundary conditions and a partially reflecting end, extending previous rational case results and connecting to Wilson polynomials.

Contribution

It generalizes the Izergin-Korepin method to the trigonometric case and provides a determinant formula involving Wilson polynomials for the number of states.

Findings

Partition function expressed as a determinant of Wilson polynomials

Extension of Foda and Zarembo's rational case to trigonometric case

Connection to ASM-like matrices

Abstract

The trigonometric six-vertex model with domain wall boundary conditions and one partially reflecting end on a lattice of size $2n\times m$, $m\leq n$, is considered. The partition function is computed using the Izergin-Korepin method, generalizing the result of Foda and Zarembo from the rational to the trigonometric case. Thereafter we specify the parameters in Kuperberg's way to get a formula for the number of states as a determinant of Wilson polynomials. We relate this to a type of ASM-like matrices.