New differential equations in the six-vertex model

TL;DR

This paper introduces a new system of PDEs for the six-vertex model's partition function, revealing novel determinant formulas and connecting to the Knizhnik-Zamolodchikov equation, advancing theoretical understanding of the model.

Contribution

It presents a new PDE framework for the six-vertex model and derives novel determinant representations, linking the model to well-known equations in mathematical physics.

Findings

Partition function satisfies a system of PDEs similar to Knizhnik-Zamolodchikov equations.

Derived new determinant formulas for the partition function.

Established theoretical connections between the six-vertex model and integrable PDEs.

Abstract

This letter is concerned with the analysis of the six-vertex model with domain-wall boundaries in terms of partial differential equations (PDEs). The model's partition function is shown to obey a system of PDEs resembling the celebrated Knizhnik-Zamolodchikov equation. The analysis of our PDEs naturally produces a family of novel determinant representations for the model's partition function.