Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

Physical Review A 90, 012508 (2014)

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

Michael Ruggenthaler, Johannes Flick, Camilla Pellegrini, Heiko Appel, Ilya V. Tokatly,, Angel Rubio

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 density-functional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photon field. 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.

Additional Information

Download
Preprint - 1.39 MB
Doi
http://dx.doi.org/10.1103/PhysRevA.90.012508
Notes
M.R. acknowledges useful discussions with C. Genes and H. Ritsch and financial support by the Austrian Science Fund (FWF Projects No. J 3016-N16 and No. P 25739-N27). We further acknowledge financial support from the European Research Council Advanced Grant DYNamo (Grant No. ERC-2010-AdG-267374), Spanish Grant (Grant No.FIS2010-21282-C02-01), Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT578-13), Ikerbasque, and the European Commission projects CRONOS (Grant No.280879-2 CRONOS CP-FP7).

Related Projects

Related Research Areas