Abstract
For certain correlated electron–photon systems we construct the exact density-to-potential maps, which are the basic ingredients of a density-functional reformulation of coupled matter-photon problems. We do so for numerically exactly solvable models consisting of up to four fermionic sites coupled to a single photon mode. We show that the recently introduced concept of the intra-system steepening (Dimitrov et al 2016 New J. Phys. 18 083004) can be generalized to coupled fermion-boson systems and that the intra-system steepening indicates strong exchange-correlation effects due to the coupling between electrons and photons. The reliability of the mean-field approximation to the electron–photon interaction is investigated and its failure in the strong coupling regime analyzed. We highlight how the intra-system steepening of the exact density-to-potential maps becomes apparent also in observables such as the photon number or the polarizability of the electronic subsystem. We finally show that a change in functional variables can make these observables behave more smoothly and exemplify that the density-to-potential maps can give us physical insights into the behavior of coupled electron–photon systems by identifying a very large polarizability due to ultra-strong electron–photon coupling.
Highlights
Recent experiments [1,2,3,4,5,6,7,8,9] at the interface of quantum chemistry, material science and quantum optics allow to tailor the physical and chemical properties of the system by coupling light strongly to the matter, e.g. by placing it in an optical cavity
Can we analyze the correlation and localization in a similar manner for coupled electron-photon system, and is the intra-system steepening a general feature of correlated systems? In this work, we construct the exact density-to-potential maps of ground-state quantum electrodynamical density-functional theory (QEDFT) [15] and examine the intrasystem steepening related to the real-space properties of the exact xc potentials for correlated electron-photon systems
We have identified the appearance of new normal modes in the coupled matter-photon system and showed how the density-to-potential maps can be constructed for all possible external pairs from only knowing the map along the polaritonic external potential vext
Summary
Recent experiments [1,2,3,4,5,6,7,8,9] at the interface of quantum chemistry, material science and quantum optics allow to tailor the physical and chemical properties of the system by coupling light strongly to the matter, e.g. by placing it in an optical cavity. The simplest approximation to the fully coupled problem and the starting point for the Kohn-Sham construction in the electron-photon case is the mean-field approximation [16] that is given by vM = −ωλqdand leads to the following Hamiltonian in the case of a two-site lattice
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