Gauge invariance and Ward identities in nonlinear response theory

Habib Rostami; Mikhail I. Katsnelson; Giovanni Vignale; Marco Polini

doi:10.1016/j.aop.2021.168523

Gauge invariance and Ward identities in nonlinear response theory

Habib Rostami, Mikhail I. Katsnelson, Giovanni Vignale, Marco Polini

Department of Physics

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19 Citations (SciVal)

Abstract

We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in real time, can be obtained from the analytic continuation of time-ordered response functions, which are more easily amenable to diagrammatic calculation. This generalizes the well-known result of linear response theory. We then use gauge invariance arguments to derive exact relations between second-order response functions in density and current channels. These identities, which are non-perturbative in the strength of inter-particle interactions, allow us to establish exact connections between nonlinear optics calculations done in different electromagnetic gauges.

Original language	English
Article number	168523
Journal	Annals of Physics
Volume	431
Early online date	27 May 2021
DOIs	https://doi.org/10.1016/j.aop.2021.168523
Publication status	Published - 1 Aug 2021

Bibliographical note

Publisher Copyright:
© 2021 The Author(s)

Funding

This work was partially supported by the European Union's Horizon 2020 research and innovation programme under grant No. 881603 (GrapheneCore3). The work of M. I. K. is supported by European Research Council via Synergy Grant No. 854843 - FASTCORR. G. V. was supported by the U.S. Department of Energy (Office of Science) under Grant DE- FG02-05ER46203. H. R. acknowledges the support from the Swedish Research Council (VR 2018-04252). This work was partially supported by the European Union’s Horizon 2020 research and innovation programme under grant No. 881603 (GrapheneCore3). The work of M. I. K. is supported by European Research Council via Synergy Grant No. 854843 - FASTCORR. G. V. was supported by the U.S. Department of Energy (Office of Science) under Grant DE- FG02-05ER46203 . H. R. acknowledges the support from the Swedish Research Council ( VR 2018-04252 ).

Funders	Funder number
US Department of Energy
Parliamentary Office of Science and Technology	DE- FG02-05ER46203
Horizon 2020 Framework Programme	854843
European Research Council
Vetenskapsrådet	VR 2018-04252
Horizon 2020	881603

Keywords

Gauge invariance
Nonlinear optics
Ward identity

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/j.aop.2021.168523Licence: CC BY

Cite this

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AB - We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in real time, can be obtained from the analytic continuation of time-ordered response functions, which are more easily amenable to diagrammatic calculation. This generalizes the well-known result of linear response theory. We then use gauge invariance arguments to derive exact relations between second-order response functions in density and current channels. These identities, which are non-perturbative in the strength of inter-particle interactions, allow us to establish exact connections between nonlinear optics calculations done in different electromagnetic gauges.

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Gauge invariance and Ward identities in nonlinear response theory

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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