Elliptic free-fermion model with OS boundary and elliptic Pfaffians

TL;DR

This paper introduces a new class of elliptic free-fermionic face model partition functions with OS boundary, expressing them explicitly via elliptic Pfaffians and establishing identities between these Pfaffians.

Contribution

It provides explicit elliptic Pfaffian formulas for partition functions with OS boundary and derives identities between different elliptic Pfaffians, advancing understanding of elliptic integrable models.

Findings

Explicit elliptic Pfaffian formulas for OS boundary partition functions

Two different expressions based on Korepin's method

An identity between two elliptic Pfaffians

Abstract

We introduce and study a class of partition functions of an elliptic free-fermionic face model. We study the partition functions with a triangular boundary using the off-diagonal $K$-matrix at the boundary (OS boundary), which was introduced by Kuperberg as a class of variants of the domain wall boundary partition functions. We find explicit forms of the partition functions with OS boundary using elliptic Pfaffians. We find two expressions based on two versions of Korepin's method, and we obtain an identity between two elliptic Pfaffians as a corollary.