Factorization of rational six vertex model partition functions

TL;DR

This paper derives new factorization formulas for rational six vertex model partition functions under various boundary conditions, enabling explicit determinant representations and broadening understanding of these integrable models.

Contribution

It introduces novel factorization formulas for partition functions with triangular and trapezoid boundaries, extending previous explicit forms and applications.

Findings

Factorization formulas for partition functions under triangular boundary.

Extension of factorization to trapezoid boundary conditions.

Determinant representations for emptiness formation probabilities.

Abstract

We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with the explicit forms of the generalized domain wall boundary partition functions by Belliard-Pimenta-Slavnov, we derive factorization formulas for partition functions under trapezoid boundary which can be viewed as a generalization of triangular boundary. We also discuss an application to emptiness formation probabilities under trapezoid boundary which admit determinant representations.