Binary trees, coproducts, and integrable systems

TL;DR

This paper introduces a unified algebraic framework for generalized mean field integrable systems, extending classical and quantum results through coproducts and binary trees, exemplified by a spin octahedron.

Contribution

It generalizes previous integrable system results using algebraic structures like coproducts and binary trees, unifying classical and quantum cases.

Findings

Unified algebraic framework for integrable systems

Extension of classical and quantum results

Application to spin octahedron

Abstract

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.