Measurable spectra are often derived from contractions of many-body Green's functions. One calculates hence more information than needed. Here we present and illustrate an in principle exact approach to construct effective potentials and kernels for the direct calculation of electronic spectra. In particular, a dynamical but local and real potential yields the spectral function needed to describe photoemission. We discuss for model solids the frequency dependence of this "photoemission potential" stemming from the nonlocality of the corresponding self-energy.
Measurable spectra are often derived from contractions of many-body Green's functions. One calculates hence more information than needed. Here we present and illustrate an in principle exact approach to construct effective potentials and kernels for the direct calculation of electronic spectra. In particular, a dynamical but local and real potential yields the spectral function needed to describe photoemission. We discuss for model solids the frequency dependence of this "photoemission potential" stemming from the nonlocality of the corresponding self-energy.
We present a method for the calculation of photoemission spectra in terms of reduced density matrices. We start from the spectral representation of the one-body Green's function G, whose imaginary part is related to photoemission spectra, and we introduce a frequency-dependent effective energy that accounts for all the poles of G. Simple approximations to this effective energy give accurate spectra in model systems in the weak as well as strong correlation regime. In real systems reduced density matrices can be obtained from reduced density-matrix functional theory. Here we use this approach to calculate the photoemission spectrum of bulk NiO: our method yields a qualitatively correct picture both in the antiferromagnetic and paramagnetic phases, contrary to mean-field methods, in which the paramagnet is a metal.
We present an original strategy for the calculation of direct and inverse photo-emission spectra from first principles. The main goal is to go beyond the standard Green's function approaches, such as the GW method, in order to find a good description not only of the quasiparticles but also of the satellite structures, which are of particular importance in strongly correlated materials. To this end we use as a key quantity the three-body Green's function, or, more precisely, its hole-hole-electron and electron-electron-hole parts, and we show how the one-body Green's function, and hence the corresponding spectral function, can be retrieved from it. We show that, contrary to the one-body Green's function, information about satellites is already present in the non-interacting three-body Green's function. Therefore, simple approximations to the three-body self-energy, which is defined by the Dyson equation for the three-body Green's function and which contains many-body effects, can still yield accurate spectral functions. In particular, the self-energy can be chosen to be static which could simplify a self-consistent solution of the Dyson equation. We give a proof of principle of our strategy by applying it to the Hubbard dimer, for which the exact self-energy is available.
The Kohn-Sham system is the prototypical example of an auxiliary system that targets, in principle exactly, an observable like the electronic density without the need to calculate the complicated many-body wavefunction. Although the Kohn-Sham system does not describe excited-state properties directly, it also represents a very successful strategy guideline for many spectroscopy applications. Here we propose a generalization of the Kohn-Sham idea. In many situations one is interested only in limited answers to specific questions, whereas in state-of-the-art approaches a lot of information is generally calculated that is not needed for the interpretation of experimental spectra. For example, when the target is a spectrum S(ω) like the optical absorption of a solid, within time-dependent density-functional theory (TDDFT) one calculates the whole response function χ(r,r',ω). Analogously, within many-body perturbation theory (MBPT) one calculates the whole one-particle Green's function G(r,r',ω), while only the total spectral function A(ω) is needed for angle-integrated photoemission spectra. In this contribution, we advocate the possibility of designing auxiliary systems with effective potentials or kernels that target only the specific spectral properties of interest and are simpler than the self-energy of MBPT or the exchange-correlation kernel of TDDFT. In particular, we discuss the fundamentals and prototypical applications of simplified effective kernels for optical absorption and spectral potentials for photoemission, and we discuss how to express these potentials or kernels as functionals of the density.
We present an original approach for the calculation of direct and inverse photo-emission spectra from first principles. The main goal is to go beyond the standard Green's function approaches, such as the GW method, in order to find a good description not only of the quasiparticles but also of the satellite structures, which are of particular importance in strongly correlated materials. Our method uses as a key quantity the three-body Green's function, or, more precisely, its hole-hole-electron and electron-electron-hole parts. We show that, contrary to the one-body Green's function, satellites are already present in the corresponding non-interacting Green's function. Therefore, simple approximations to the three-body self-energy, which is defined by the Dyson equation for the three-body Green's function and which contains many-body effects, can still yield accurate spectral functions. In particular, the self-energy can be chosen to be static which could simplify a self-consistent solution of the Dyson equation. We also show how the one-body Green's function can be retrieved from the three-body Green's function. We illustrate our approach by applying it to the symmetric Hubbard dimer.
We present the multi-channel Dyson equation that combines two or more many-body Green's functions to describe the electronic structure of materials. In this work we use it to model photoemission spectra by coupling the one-body Green's function with the three-body Green's function. We demonstrate that, unlike methods using only the one-body Green's function, our approach puts the description of quasiparticles and satellites on an equal footing. We propose a multi-channel self-energy that is static and only contains the bare Coulomb interaction, making frequency convolutions and self-consistency unnecessary. Despite its simplicity, we demonstrate with a diagrammatic analysis that the physics it describes is extremely rich. Finally, we present a framework based on an effective Hamiltonian that can be solved for any many-body system using standard numerical tools. We illustrate our approach by applying it to the Hubbard dimer and show that it is exact both at 1/4 and 1/2 filling.
In time-dependent density-functional theory, an important quantity is the exchange-correlation kernel whose knowledge allows for the calculations of the excitation spectrum of electronic systems. In most applications, the exchange-correlation kernel is approximated by the adiabatic local-density approximation, ignoring the frequency dependence and nonlocality. To gain insight into the nature of the exact exchange-correlation kernel, we have considered a two-dimensional one-band Hubbard model. The calculated exact exchange-correlation kernel reveals a number of striking features. It has a weak energy dependence up to the main excitation energy. On the other hand, the exact kernel shows a strong energy dependence in energy regions, where there are many-body excitations that are not contained in the local-density approximation, even though these excitations have small weight. It is found that a static approximation can well reproduce the main excitation peaks, but the satellite structures arising from many-body interaction are unlikely to be accounted for with a static approximation.