Scalar products of the elliptic Felderhof model and elliptic Cauchy formula

TL;DR

This paper derives a determinant formula for scalar products in the elliptic Felderhof model, leading to a Cauchy formula for elliptic Schur functions, advancing the understanding of elliptic integrable models.

Contribution

It introduces a determinant formula for scalar products in the elliptic Felderhof model and connects it to elliptic Schur functions, extending existing integrable model techniques.

Findings

Determinant formula for scalar products derived

Cauchy formula for elliptic Schur functions established

Enhanced understanding of elliptic integrable models achieved

Abstract

We analyze the scalar products of the elliptic Felderhof model introduced by Foda-Wheeler-Zuparic as an elliptic extension of the trigonometric face-type Felderhof model by Deguchi-Akutsu. We derive the determinant formula for the scalar products by applying the Izergin-Korepin technique developed by Wheeler to investigate the scalar products of integrable lattice models. By combining the determinant formula for the scalar products with the recently-developed Izergin-Korepin technique to analyze the wavefunctions, we derive a Cauchy formula for elliptic Schur functions.