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On non-canonical degrees of freedom

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.
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https://hal.archives-ouvertes.fr/hal-02973159
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Submitted on : Tuesday, October 20, 2020 - 10:19:58 PM
Last modification on : Tuesday, May 4, 2021 - 10:52:06 PM

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Eoin Quinn. On non-canonical degrees of freedom. SciPost Phys., 2021, 10, pp.075. ⟨10.21468/SciPostPhys.10.3.075⟩. ⟨hal-02973159⟩

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