Interacting and noninteracting integrable systems

TL;DR

This paper proposes characterizing integrable systems as interacting or noninteracting based on the Onsager matrix, with zero indicating noninteracting systems, supported by analysis of classical and quantum chains.

Contribution

It introduces a new criterion using the Onsager matrix to distinguish between interacting and noninteracting integrable systems.

Findings

Zero Onsager matrix characterizes noninteracting systems

Classical and quantum chains analyzed support the proposed criterion

Provides a unified framework for understanding integrability types

Abstract

The distinction between interacting and noninteracting integrable systems is proposed to be characterized by the Onsager matrix. It being zero is the defining property of a noninteracting integrable system. To support our view we discuss various classical and quantum integrable chains.