Supersymmetric Vertex Models with Domain Wall Boundary Conditions

TL;DR

This paper derives determinant formulas for partition functions of supersymmetric vertex models with domain wall boundary conditions, simplifying to basic functions in the homogeneous limit, advancing understanding of these models.

Contribution

It introduces determinant representations for supersymmetric vertex models with domain wall boundary conditions using Drinfeld twists, a novel approach in this context.

Findings

Determinant formulas for $gl(1|1)$ and $gl(2|1)$ models derived.

Determinants simplify to basic functions in the homogeneous limit.

Provides a new method for analyzing supersymmetric vertex models.

Abstract

By means of the Drinfeld twists, we derive the determinant representations of the partition functions for the $gl(1|1)$ and $gl(2|1)$ supersymmetric vertex models with domain wall boundary conditions. In the homogenous limit, these determinants degenerate to simple functions.