Multichannel Dyson Equation: Coupling Many-Body Green's Functions.

We present the multichannel 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.

The three channels of many-body perturbation theory: GW, particle-particle, and electron-hole T-matrix self-energies.

We derive the explicit expression of the three self-energies that one encounters in many-body perturbation theory: the well-known GW self-energy, as well as the particle-particle and electron-hole T-matrix self-energies. Each of these can be easily computed via the eigenvalues and eigenvectors of a different random-phase approximation linear eigenvalue problem that completely defines their corresponding response function. For illustrative and comparative purposes, we report the principal ionization potentials of a set of small molecules computed at each level of theory.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Static and dynamic Bethe-Salpeter equations in the T-matrix approximation.

While the well-established GW approximation corresponds to a resummation of the direct ring diagrams and is particularly well suited for weakly correlated systems, the T-matrix approximation does sum ladder diagrams up to infinity and is supposedly more appropriate in the presence of strong correlation. Here, we derive and implement, for the first time, the static and dynamic Bethe-Salpeter equations when one considers T-matrix quasiparticle energies and a T-matrix-based kernel. The performance of the static scheme and its perturbative dynamical correction are assessed by computing the neutral excited states of molecular systems.

Time dependent reduced density matrix functional theory at strong correlation: insights from a two-site Anderson impurity model.

The one-body density matrix has recently attracted considerable attention as a promising key quantity for the description of systems out of equilibrium. Its time evolution is given in terms of the two-body density matrix, and thus the central challenge is to find approximations to the latter. An extra layer of difficulty is added when dealing with strong electron correlations.

Potential Energy Surfaces without Unphysical Discontinuities: The Coulomb Hole Plus Screened Exchange Approach.

In this work, we show the advantages of using the Coulomb hole plus screened exchange (COHSEX) approach in the calculation of potential energy surfaces (PES). In particular, we demonstrate that, unlike perturbative and partial self-consistent approaches, such as eigenvalue self-consistent and quasi-particle (QP) self-consistent , the COHSEX approach yields smooth PES without irregularities and discontinuities. Moreover, we show that the ground-state PES obtained from the Bethe-Salpeter equation (BSE), within the adiabatic connection fluctuation dissipation theorem, built with QP energies obtained from perturbative COHSEX on top of Hartree-Fock (BSE@COHSEX@HF) yield very accurate results for diatomic molecules close to their equilibrium distance.

Unphysical Discontinuities in GW Methods.

We report unphysical irregularities and discontinuities in some key experimentally measurable quantities computed within the GW approximation of many-body perturbation theory applied to molecular systems. In particular, we show that the solution obtained with partially self-consistent GW schemes depends on the algorithm one uses to self-consistently solve the quasiparticle (QP) equation. The main observation of the present study is that each branch of the self-energy is associated with a distinct QP solution and that each switch between solutions implies a significant discontinuity in the quasiparticle energy as a function of the internuclear distance.

Green Functions and Self-Consistency: Insights From the Spherium Model.

We report an exhaustive study of the performance of different variants of Green function methods for the spherium model in which two electrons are confined to the surface of a sphere and interact via a genuine long-range Coulomb operator. We show that the spherium model provides a unique paradigm to study electronic correlation effects from the weakly correlated regime to the strongly correlated regime, since the mathematics are simple while the physics is rich. We compare perturbative GW, partially self-consistent GW and second-order Green function (GF2) methods for the computation of ionization potentials, electron affinities, energy gaps, correlation energies as well as singlet and triplet neutral excitations by solving the Bethe-Salpeter equation (BSE).

Many-body perturbation theory and non-perturbative approaches: screened interaction as the key ingredient.

Many-body perturbation theory is often formulated in terms of an expansion in the dressed instead of the bare Green's function, and in the screened instead of the bare Coulomb interaction. However, screening can be calculated on different levels of approximation, and it is important to define what is the most appropriate choice. We explore this question by studying a zero-dimensional model (so called 'one-point model') that retains the structure of the full equations.

Gauge-Invariant Formulation of Circular Dichroism.

Standard formulations of magnetic response properties, such as circular dichroism spectra, are plagued by gauge dependencies, which can lead to unphysical results. In this work, we present a general gauge-invariant and numerically efficient approach for the calculation of circular dichroism spectra from the current density. First we show that in this formulation the optical rotation tensor, the response function from which circular dichroism spectra can be obtained, is independent of the origin of the coordinate system.

Gauge-invariant calculation of static and dynamical magnetic properties from the current density.

In this work we solve two problems related to the calculation of static and dynamical magnetic properties with ab initio theories. First, we show that the dependence of the dynamical magnetic dipole moment on the reference point of the multipole expansion and on the gauge origin of the vector potential have a clear physical significance. They are due to a dynamical electric dipole moment and an electric field, respectively.

Valence electron photoemission spectrum of semiconductors: ab initio description of multiple satellites.

The experimental valence band photoemission spectrum of semiconductors exhibits multiple satellites that cannot be described by the GW approximation for the self-energy in the framework of many-body perturbation theory. Taking silicon as a prototypical example, we compare experimental high energy photoemission spectra with GW calculations and analyze the origin of the GW failure. We then propose an approximation to the functional differential equation that determines the exact one-body Green's function, whose solution has an exponential form.

Double excitations in correlated systems: a many–body approach.

A coherent approach to the description of double excitations in correlated materials is presented: We derive stringent mathematical conditions on the algebraical structure of the Bethe–Salpeter and time-dependent density functional theory kernels that avoid the occurrence of spurious and nonphysical excitations. We discuss how these conditions need to be respected at any level of approximation, including the commonly used local density and static screening approximations. We propose a correlated kernel for the Bethe–Salpeter equation, and we illustrate several aspects of our approach with numerical calculations for model molecular systems.

Double excitations in correlated systems: a many-body approach.

A coherent approach to the description of double excitations in correlated materials is presented: We derive stringent mathematical conditions on the algebraical structure of the Bethe-Salpeter and time-dependent density functional theory kernels that avoid the occurrence of spurious and nonphysical excitations. We discuss how these conditions need to be respected at any level of approximation, including the commonly used local density and static screening approximations. We propose a correlated kernel for the Bethe-Salpeter equation, and we illustrate several aspects of our approach with numerical calculations for model molecular systems.