Perfect Integrability and Gaudin Models

TL;DR

This paper introduces the concept of perfect integrability in quantum spin chains and demonstrates it for Gaudin models linked to all finite simple Lie algebras, under various boundary conditions.

Contribution

It proposes the notion of perfect integrability for quantum spin chains and proves it for Gaudin models across all finite simple Lie algebras.

Findings

Gaudin models are perfectly integrable for all finite simple Lie algebras.

Perfect integrability extends to models with periodic and quasi-periodic boundary conditions.

Abstract

We suggest the notion of perfect integrability for quantum spin chains and conjecture that quantum spin chains are perfectly integrable. We show the perfect integrability for Gaudin models associated to simple Lie algebras of all finite types, with periodic and regular quasi-periodic boundary conditions.