Exact functionals for correlated electron–photon systems

Abstract

For certain correlated electron-photon systems we construct the exact\ndensity-to-potential maps, which are the basic ingredients of a\ndensity-functional reformulation of coupled matter-photon problems. We do so\nfor numerically exactly solvable models consisting of up to four fermionic\nsites coupled to a single photon mode. We show that the recently introduced\nconcept of the intra-system steepening (T.Dimitrov et al., 18, 083004 NJP\n(2016)) can be generalized to coupled fermion-boson systems and that the\nintra-system steepening indicates strong exchange-correlation (xc) effects due\nto the coupling between electrons and photons. The reliability of the\nmean-field approximation to the electron-photon interaction is investigated and\nits failure in the strong coupling regime analyzed. We highlight how the\nintra-system steepening of the exact density-to-potential maps becomes apparent\nalso in observables such as the photon number or the polarizability of the\nelectronic subsystem. We finally show that a change in functional variables can\nmake these observables behave more smoothly and exemplify that the\ndensity-to-potential maps can give us physical insights into the behavior of\ncoupled electron-photon systems by identifying a very large polarizability due\nto ultra-strong electron-photon coupling.\n