Capturing strong correlations in spin, electron and local moment systems

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.

Misleading and erroneous discussions in Secs. 3 and 8. The content of Secs. 4-7 can alternatively be found in Sec. 2 and App. A of arXiv:2009.14755