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Electromagnetic coupling in tight-binding models for strongly correlated light and matter

Jiajun Li, Denis Golez, Giacomo Mazza, Andrew J. Millis, Antoine Georges, and Martin Eckstein
Phys. Rev. B 101, 205140 – Published 21 May 2020

Abstract

We discuss the construction of low-energy tight-binding Hamiltonians for condensed-matter systems with a strong coupling to the quantum electromagnetic field. Such Hamiltonians can be obtained by projecting the continuum theory on a given set of Wannier orbitals. However, different representations of the continuum theory lead to different low-energy formulations because different representations may entangle light and matter, transforming orbitals into light-matter hybrid states before the projection. In particular, a multicenter Power-Zienau-Woolley transformation yields a dipolar Hamiltonian which incorporates the light-matter coupling via both Peierls phases and a polarization density. We compare this dipolar gauge Hamiltonian and the straightforward Coulomb gauge Hamiltonian for a one-dimensional solid to describe subcycle light-driven electronic motion in the semiclassical limit and a coupling of the solid to a quantized cavity mode which renormalizes the band-structure into electron-polariton bands. Both descriptions yield the same result when many bands are taken into account but the dipolar Hamiltonian is more accurate when the model is restricted to few electronic bands, while the Coulomb Hamiltonian requires fewer electromagnetic modes.

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  • Received 28 January 2020
  • Revised 3 April 2020
  • Accepted 4 May 2020

DOI:https://doi.org/10.1103/PhysRevB.101.205140

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Jiajun Li1, Denis Golez2, Giacomo Mazza3,4,5, Andrew J. Millis2,6, Antoine Georges5,2,4,3, and Martin Eckstein1

  • 1Department of Physics, University of Erlangen-Nürnberg, 91058 Erlangen, Germany
  • 2Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
  • 3Department of Quantum Matter Physics, University of Geneva, 1211 Geneva 4, Switzerland
  • 4CPHT, CNRS, Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France
  • 5Collège de France, 11 Place Marcelin Berthelot, 75005 Paris, France
  • 6Department of Physics, Columbia University 538 West 120th Street, New York, New York 10027, USA

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Issue

Vol. 101, Iss. 20 — 15 May 2020

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