# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1906.08251