On the partition function of the six-vertex model with domain wall boundary conditions

TL;DR

This paper provides a Fredholm determinant representation for the partition function of the six-vertex model with domain wall boundary conditions, linking it to classical orthogonal polynomials and quantum operator traces.

Contribution

It introduces a novel Fredholm determinant formula with an integrable kernel involving orthogonal polynomials and a reconstruction method using quantum operators.

Findings

Fredholm determinant representation of the partition function

Kernel involves classical orthogonal polynomials

Reconstruction formula as trace of quantum operator

Abstract

The six-vertex model on an $N\times N$ square lattice with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is given. The kernel of the corresponding integral operator is of the so-called integrable type, and involves classical orthogonal polynomials. From this representation, a ``reconstruction'' formula is proposed, which expresses the partition function as the trace of a suitably chosen quantum operator, in the spirit of corner transfer matrix and vertex operator approaches to integrable spin models.