Capturing strong correlations in spin, electron and local moment systems

TL;DR

This paper explores non-canonical algebraic frameworks to identify quantum degrees of freedom in correlated systems, extending beyond traditional bosonic or fermionic quasi-particle descriptions.

Contribution

It introduces a new class of non-canonical algebras for spin, electron, and local moment systems, broadening the scope of quasi-particle theories in strongly correlated matter.

Findings

Highlights the usefulness of non-canonical algebras in quantum systems

Provides a broad overview of algebraic frameworks for correlated systems

Outlines test problems for developing these algebraic approaches

Abstract

We address the question of identifying degrees of freedom for quantum systems. Typically, quasi-particle descriptions of correlated matter are based upon the canonical algebras of bosons or fermions. Here we highlight that a special class of non-canonical algebras also offer useful quantum degrees of freedom, allowing for the development of quasi-particle descriptions which go beyond the weakly correlated paradigm. We give a broad overview of such algebras for spin, electron and local moment systems, and outline important test problems upon which to develop the framework.