The Hidden Quantum Group of the 8-vertex Free Fermion Model: q-Clifford Algebras

TL;DR

This paper demonstrates that the elliptic R-matrix of the 8-vertex free fermion model is an intertwiner of a quantum deformed Clifford-Hopf algebra, constructed via affinization of a quantum Clifford algebra deformation.

Contribution

It introduces a new quantum deformed Clifford-Hopf algebra framework that explains the elliptic R-matrix in the 8-vertex free fermion model.

Findings

Elliptic R-matrix is an intertwiner of a quantum deformed Clifford-Hopf algebra.

Construction of the algebra via affinization of a quantum Clifford algebra.

Establishes a new algebraic structure underlying the 8-vertex free fermion model.

Abstract

We prove in this paper that the elliptic $R$--matrix of the eight vertex free fermion model is the intertwiner $R$--matrix of a quantum deformed Clifford--Hopf algebra. This algebra is constructed by affinization of a quantum Hopf deformation of the Clifford algebra.