Switch Operators for the Six-Vertex Model

TL;DR

This paper introduces a new switch operator for the six-vertex model, enabling the expression of partition functions with arbitrary boundaries and deriving explicit formulas for factorial Schur functions, thus deepening understanding of boundary effects.

Contribution

It presents a novel switch operator based on the Yang-Baxter equation that connects different boundary conditions in the six-vertex model.

Findings

Derived explicit formulas for factorial Schur functions.

Expressed partition functions with arbitrary boundaries in terms of domain wall boundary conditions.

Provided new insights into boundary condition effects on partition functions.

Abstract

In this paper, we introduce and analyze a new switch operator for the six-vertex model. This operator, derived from the Yang-Baxter equation, allows us to express the partition function with arbitrary boundaries in terms of a base case with domain wall boundary conditions. As an application, we derive explicit formulas for the factorial Schur functions and their generalizations. Our results provide new insights into the relationship between boundary conditions and partition functions in the six-vertex model.