Long-range excitations in time-dependent density functional theory

Normand A. Modine, Cheng‐Wei Lee, André Schleife

Ayako Nakata, Takao Tsuneda, Kimihiko Hirao

Peter Schmitteckert, Michael Dzierzawa, Peter F. H. Schwab

We employ the density matrix renormalization group to construct the exact time-dependent exchange-correlation potential for an impurity model with an applied transport voltage. Even for short-ranged interaction we find an infinitely long-ranged exchange-correlation potential which is built up instantly after switching on the voltage. Our result demonstrates the fundamental difficulties of transport calculations based on time-dependent density functional theory. While formally the approach works, important information can be missing in the ground-state functionals and may be hidden in the usually unknown non-equilibrium functionals.

Aurel Bulgac, Michael McNeil Forbes

Ralf Stubner

The density-functional theory (DFT) is one of the most important ab initio methods for calculating properties of many-body systems. The success of DFT is based on the Kohn-Sham (KS) method and the approximations for the exchange-correlation (xc) effects. These approximations are well understood. However, DFT is first and foremost a theory for the ground state. It is very difficult to obtain properties of excited states. The time-dependent density-functional theory (TDDFT) can overcome this restriction and in the linear-response regime can give access to the properties of excited states. However, the xc effects, which are contained in the xc kernel f_xc , have to be approximated. The approximations for f_xc are not well understood up to now. Green-functions-based conventional many-body theory (MBT) is an alternative approach to the many-body problem. Especially when combined with diagrammatic techniques, MBT allows to derive physically motivated approximations. This work investigates the use of diagrammatic techniques from MBT for TDDFT . The aim of the investigations is to contribute to the development, testing, and understanding of the approximations involved in the time-dependent case. It is shown that it is possible to expand the xc kernel in a diagrammatic series. Explicit diagrammatic rules for constructing f_xc in any order of the perturbation theory are given. The derived diagrammatic rules enable us to study the analytic properties of f_xc. It is shown that f_xc is finite at KS excitation energies in every order of the perturbation theory. If this were not the case, finite-order approximations to f_xc would not give sensible results for the kernel which plays the role of a mass operator connecting the KS density--density response function with the exact density--density response function. However, there is one important difference between f_xc and the self-energy, the latter playing the role of the mass operator connecting free and exact Green function. This becomes apparent when the perturbative expansion for f_xc is used to calculate the correction to the KS excitation energies. This correction is obtained up to the second-order with respect to the interaction and with respect to one- and two-particle irreducible elements. It is shown that if a perturbative approximation for f_xc is used, the correction to the KS excitation energies has to be calculated using a consistent approach based on the same order of perturbation theory for both quantities. One of the most promising applications of TDDFT in the linear response regime is the calculation of electronic excitation spectra of solids, where TDDFT could replace the computationally expensive solution of the BSE , which is normally used for describing the excitonic correlations. It is shown that the xc kernel can be separated into a quasiparticle and a excitonic part in an exact and unambiguous way. The diagrammatic rules derived for f_xc apply to these parts separately. This allows us to express the excitonic part in terms of the three-point function, for which an integral equation is derived. This integral equation is similar to the BSE and gives the exact translation of the BSE into the TDDFT language. There exists the possibility of cancellation effects in the kernel of the integral equation. If these effects are effective, a first-order approximation to the excitonic f_xc is sufficient. The cancellation effects in the equation for Lambda are explicitly studied for a two-band model semiconductor. Using a general short-range interaction between the quasiparticles (QPs) all relevant equations are solved analytically. It is shown that the cancellation is most effective directly at the band-gap energy. Consequently, the first-order and the exact excitonic f_xc are very similar close to the band-gap energy for all interaction strengths. For a weak interaction the first-order approximation to the excitonic f_xc describes the different excitonic correlations in the density©density response function very well. Qualitatively similar results are found when the QPs interact via the long-ranged Coulomb interaction.

Takao Tsuneda, Kimihiko Hirao