On non-canonical degrees of freedom

TL;DR

This paper explores the theoretical framework of non-canonical degrees of freedom in condensed matter physics, proposing new analytical tools and discussing their implications for understanding complex electronic phenomena.

Contribution

It introduces a novel closed-form expression for a self-energy-like object and develops analogues of RPA and GW approximations for non-canonical degrees of freedom.

Findings

Derived a new self-energy expression for non-canonical degrees

Developed RPA and GW analogues for non-canonical systems

Highlighted challenges in higher-order, conservation-law consistent approximations

Abstract

Non-canonical degrees of freedom provide one of the most promising routes towards characterising a range of important phenomena in condensed matter physics. Potential candidates include the pseudogap regime of the cuprates, heavy-fermion behaviour, and also indeed magnetically ordered systems. Nevertheless it remains an open question whether non-canonical algebras can in fact provide legitimate quantum degrees of freedom. In this manuscript we survey progress made on this topic, complementing distinct approaches so as to obtain a unified description. In particular we obtain a novel closed-form expression for a self-energy-like object for non-canonical degrees of freedom. We further make a resummation of density correlations to obtain analogues of the RPA and GW approximations commonly employed for canonical degrees of freedom. We discuss difficulties related to generating higher-order approximations which are consistent with conservation laws, which represents an outstanding issue. We also discuss how the interplay between canonical and non-canonical degrees of freedom offers a useful paradigm for organising the phase diagram of correlated electronic behaviour.