The elliptic scattering theory of the 1/2-XYZ and higher order Deformed Virasoro Algebras

TL;DR

This paper analyzes bound state excitations in the spin 1/2-XYZ model using Non-Linear Integral Equations, deriving scattering factors and introducing a hierarchy of Deformed Virasoro Algebras related to elliptic breathers.

Contribution

It introduces a novel elliptic scattering theory for higher order Deformed Virasoro Algebras derived from the XYZ model's bound states.

Findings

Explicit computation of scattering factors between elliptic breathers.

Establishment of a tower of n-th order Deformed Virasoro Algebras.

Connection to the known algebra of Shiraishi-Kubo-Awata-Odake for n=1.

Abstract

Bound state excitations of the spin 1/2-XYZ model are considered inside the Bethe Ansatz framework by exploiting the equivalent Non-Linear Integral Equations. Of course, these bound states go to the sine-Gordon breathers in the suitable limit and therefore the scattering factors between them are explicitly computed by inspecting the corresponding Non-Linear Integral Equations. As a consequence, abstracting from the physical model the Zamolodchikov-Faddeev algebra of two $n$-th elliptic breathers defines a tower of $n$-order Deformed Virasoro Algebras, reproducing the $n=1$ case the usual well-known algebra of Shiraishi-Kubo-Awata-Odake \cite{SKAO}.