On the trigonometric Felderhof model with domain wall boundary conditions

TL;DR

This paper analyzes the trigonometric Felderhof model with domain wall boundary conditions, deriving determinant and product formulas for its partition function, and connecting it to integrable systems like the 2-Toda hierarchy.

Contribution

It provides a determinant expression for the partition function with fixed rapidities and a product form in the homogeneous limit, linking the model to integrable hierarchies.

Findings

Determinant expression for the partition function with fixed rapidities.

Product form of the partition function in the homogeneous limit.

Connection to the 2-Toda tau function.

Abstract

We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant expression for the partition function in the special case where the dependence on the rapidities is eliminated, but for general external field variables. This determinant can be evaluated in product form. In the homogeneous limit, it is proportional to a 2-Toda tau function. Next, we use the algebraic Bethe ansatz factorized basis to obtain a product expression for the partition function in the general case with dependence on all variables.