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On non-canonical degrees of freedom

by Eoin Quinn

Submission summary

As Contributors: Eoin Quinn
Preprint link: scipost_202102_00002v2
Date accepted: 2021-03-18
Date submitted: 2021-03-08 19:01
Submitted by: Quinn, Eoin
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


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.

Published as SciPost Phys. 10, 075 (2021)

Author comments upon resubmission

We hereby submit the revised manuscript, addressing the points made in the report. In addition, we felt it appropriate to modify the title from "Non-canonical degrees of freedom" to "On non-canonical degrees of freedom".

List of changes

- title is changed to "On non-canonical degrees of freedom".
- on page 7, at the end of the second last paragraph, a comment is added to highlight that in general for a given system one cannot tell a priori what the appropriate degree of freedom are.
- on page 8, at the end of the leading paragraph, the possibility of exploring non-canonical correlations in spin-orbit coupled systems is highlighted.
- on page 8, citations to Refs. [13] and [43], and an additional reference to Eq. (16), have been added to the discussion of the violation of the Luttinger sum rule. It is also now highlighted that violation of the Luttinger sum rule by the Hubbard Fermi liquid indicates that is not adiabatically connected to the Landau Fermi liquid.
- at the beginning of Sec. 5.4 on page 21 we now highlight that we set aside the question of how to generate conserving approximations when we consider the resummation of density-induced correlations.

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