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physica status solidi (b)

Many‐body perturbation theory combined with time dependent DFT: A new method for the calculation of the dielectric function of solids

Rodolfo Del Sole, Olivia Pulci, Valério Olevano, Andrea Marini

Published Oct 6, 2005• 7 citations
Publisher

Abstract

Abstract We show an approximate method to calculate the polarizability of a many‐electron system within Green's function theory in a similar way as within time‐dependent density functional theory (TDDFT). The basic idea is to join the computational simplicity of the latter with the accuracy of the former. We apply this approach to a prototype system, LiF. For comparison, we also show results obtained within other approximated TDDFT‐based methods. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200541153

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Abstract We show an approximate method to calculate the polarizability of a many‐electron system within Green's function theory in a similar way as within time‐dependent density functional theory (TDDFT). The basic idea is to join the computational simplicity of the latter with the accuracy of the former. We apply this approach to a prototype system, LiF. For comparison, we also show results obtained within other approximated TDDFT‐based methods. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We develop a method to calculate the polarizability of a many-electron system within Green's function theory in a similar way as within time-dependent density functional theory and apply it to Si and GaAs. The method joins the computational simplicity of the latter with the accuracy of the former approach. The resulting exchange-correlation many-body kernel fxcFQP{f}_{\mathrm{xc}}^{\mathrm{FQP}}fxcFQP​ and optical spectra are in good agreement with those obtained by the solution of the Bethe-Salpeter equation.
Abstract The calculation of the polarizability provides a method of calculating the collective‐modes excitation energies of an electronic system. However, the polarizability is a correlated quantity, thus demanding a major effort when Monte Carlo methods are used for its evaluation. Nevertheless, Quantum Monte Carlo results represent the benchmark in most many‐body physics. We applied a correlated Variational and Diffusion Monte Carlo scheme to a GaAs–AlGaAs quantum dot. Comparison with Raman scattering experiments and previous calculations is considerable. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Time-dependent density functional theory (TDDFT) is a standard approach for calculating optical excitations of molecules and solids, while ensemble DFT (EDFT) is a promising alternative under development. We introduce ensemble TDDFT (ETDDFT), a practical theory that combines the two, generalizing both; we ensemble generalize the Gross-Kohn equation and the exchange-correlation kernel of TDDFT, and generalize EDFT to time-dependent problems. We relate coordinate scaling to the adiabatic connection. The new theory provides multiple avenues for constructing and using approximations. We illustrate these on the two-site Hubbard model. We connect our results to the more general case of nonperturbative time dependence.
For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schrödinger equation, based on knowledge of the density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle non-interacting Schrödinger equations—the Kohn–Sham equations. The complication of the problem is hidden in the—unknown—time-dependent exchange and correlation potential that appears in the Kohn–Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local-density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, which are instead well described by solving the Bethe–Salpeter equation of many-body perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of this and thanks to recent successful developments of improved linear-response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems.
Abstract The frequency‐dependent response of a one‐dimensional fermion system is investigated using Current Density Functional Theory (CDFT) within the local approximation (LDA). DFT‐LDA, and in particular CDFT‐LDA, reproduces very well the dispersion of the collective excitations. Unsurprisingly, however, the approximation fails for details of the dynamic response for large wavevectors. In particular, we introduce CDFT for the one‐dimensional spinless fermion model with nearest‐neighbor interaction, and use CDFT‐LDA plus exact (Bethe ansatz) results for the groundstate energy as function of particle density and boundary phase to determine the linear response. The successes and failures of this approach are discussed in detail (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Accurate descriptions of the electronic properties of molecules, solids and other materials are crucial in the development of many modern technologies, and are therefore the subject of much scientific research. In tandem with experimental research, computational simulations play a huge role. Density functional theory (DFT) is the most popular method for performing ground-state electronic structure calculations due to its accuracy in many situations along with its computational efficiency. Its time-dependent extension (TDDFT) allows the modelling of the dynamics of systems of interacting electrons. (TD)DFT is an exact theory in principle, but requires approximations in practice, specifically to the many-body effects of electron exchange and correlation (xc), which are described by some unknown universal functional. Despite much success, it often proves inadequate in many scenarios of increasing interest. Therefore, we aim to contribute to the development of improved approximate density functionals. \n \nIn this thesis, we take the approach of studying small model systems for which we can compute the exact functionals. These systems are designed to exhibit the key features present in realistic quantum systems, such as atoms and molecules, which the exact universal (TD)DFT functional is capable of describing, but are often ill-described by the commonly used approximations. By analysing the nature of these exact functionals, we gain valuable insight into their fundamental properties, together with identifying where the current approximations are lacking, thereby allowing us to suggest how these approximations may be improved.