Exact functionals for correlated electron–photon systems

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 (T. Dimitrov et al., 18, 083004 NJP (2016)) can be generalized to coupled fermion-boson systems and that the intra-system steepening indicates strong exchange-correlation (xc) 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.

Polariton chemistry: controlling molecular dynamics with optical cavities

“…This allows a consistent and predictive description of the behavior of strongly coupled ensembles including a macroscopic number of molecules. First-principles approaches are explored in ref. 50, 51 and 60 .…”

Light–matter interaction in the long-wavelength limit: no ground-state without dipole self-energy

“…Here R(t) = ψ(t)|Rψ(t) and ψ(t) a purely electronic wave-function. For a static problem we therefore find, in accordance to the fact that p α actually corresponds to the displacement field, that we are left with the polarization term only, i.e., in equilibrium D = P[ψ] = ψ|P ψ and the electric field is zero as it should for an eigen-state [40,49]. If we further choose a symmetric binding potential at the origin, the eigen-states have zero dipole-moment and we reduce to the usual HamiltonianĤ e plus the dipole-self energy.…”

“…Finally, by using tot (t) = ( + A(t)) and combining both above derivations we can include also time-dependent fields. Note, however, that we can always exchange an external field by an appropriately chosen external time-dependent current [49]. To conclude, the semiclassical limit performed after the length-gauge transformations supports eigen-states due to the presence of the dipole self-energy term in contrast to the standard semi-classical limit.…”

Shedding light on correlated electron–photon states using the exact factorization

“…This approach to coupled electron-photon dynamics is complementary to the recently developed TDDFT approach to cavity QED. Indeed, the e-ph correlation potential which was the heart of our investigation in this work is closely related to the correlation potential of the cavity QED (TD)DFT, therefore, the features of the e-ph correlation potential we discussed in this work together with the analytical approximation of the potential presented here are particularly relevant for developing the cavity QED (TD)DFT exchange-correlation functionals [25,26]. Another interesting avenue to explore is the connection between the approach proposed here and the Born-Huang expansion approach for the cavity QED that has been proposed very recently [63].…”