SciPost Submission Page
Non-canonical degrees of freedom
by Eoin Quinn
|As Contributors:||Eoin Quinn|
|Date submitted:||2021-02-01 09:53|
|Submitted by:||Quinn, Eoin|
|Submitted to:||SciPost Physics|
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 paper we survey progress made on this topic, complementing distinct approaches so as to obtain a unified description. In particular we obtain a novel exact representation 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.
Author comments upon resubmission
We hereby submit the revised manuscript, addressing the points made by the referees. We hope this is ready for publication in SciPost Physics.
List of changes
- a footnote has been added in Sec. 2.2 to clarify that the splitting of the electron falls outside the classification of elementary particles coming from high-energy physics.
- in Sec. 3 it is clarified that the hopping and interaction parameters are taken to be real.
- in Sec. 3 the value of \lambda corresponding to the Heisenberg model of Eq. (31) is now specified.
- at the end of Sec. 5.2, and throughout the text, it is clarified that the closed equations specifying the self-energy-like object for non-canonical degrees of freedom take a functional differential form, and that it is through perturbative expansion of these equations that systematic approximations for the Green's function are obtained.
Submission & Refereeing History
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