Quantum electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory
By M. Ruggenthaler, Johannes Flick, C. Pellegrini, H. Appel, I. Tokatly, Á. Rubio. 2014
257 citations recorded by the source corpus.
In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the densityfunctional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photonfield. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/049529fb098c19e8821f484512c812db166f2d94
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
- F. García-Vidal
- J. Feist
- Javier Galego
- Micael J. T. Oliveira
- Miguel A. L. Marques
- Davis M. Welakuh
- V. Rokaj
- Á. Rubio
Citations in the corpus
- Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems. (2019, background): “In practice, QEDFT requires the construction of an additional exchange–correlation potential that describes the electron–photon interaction.”
- Cavity-induced modifications of molecular structure in the strong coupling regime (2015, methodology): “We note that there has been some recent progress on combining QED with density functional theory [50,51], which could provide complementary information to the model presented here.”
- Light–matter interaction in the long-wavelength limit: no ground-state without dipole self-energy (2018, methodology): “So far nonrelativistic QED has not been applied much in practice due to its inherent computational complexity, but recent approaches such as the formally exact density-functional reformulation of QED [6, 25, 26], generalized Green’s function methods [27] or extensions of quantum-chemical approximati”