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The Bethe-Salpeter equation has been extensively employed to compute the two-body electron-hole propagator and its poles which correspond to the neutral excitation energies of the system. Through a different time-ordering, the two-body Green's function can also describe the propagation of two electrons or two holes. The corresponding poles are the double ionization potentials and double electron affinities of the system. In this work, a Bethe-Salpeter equation for the two-body particle-particle propagator is derived within the linear-response formalism using a pairing field and anomalous propagators. This framework allows us to compute kernels corresponding to different self-energy approximations ($GW$, $T$-matrix, and second-Born) as in the usual electron-hole case. The performance of these various kernels is gauged for singlet and triplet valence double ionization potentials using a set of 23 small molecules. The description of double core hole states is also analyzed.
In a recent letter [Phys. Rev. Lett. 131, 216401] we presented the multichannel Dyson equation (MCDE) in which two or more many-body Green's functions are coupled. In this work we will give further details of the MCDE approach. In particular we will discuss: 1) the derivation of the MCDE and the definition of the space in which it is to be solved; 2) the rationale of the approximation to the multichannel self-energy; 3) a diagrammatic analysis of the MCDE; 4) the recasting of the MCDE on an eigenvalue problem with an effective Hamiltonian that can be solved using standard numerical techniques. This work mainly focuses on the coupling between the one-body Green's function and the three-body Green's function to describe photoemission spectra, but the MCDE method can be generalized to the coupling of other many-body Green's functions and to other spectroscopies.
Hedin's equations provide an elegant route to compute the exact one-body Green's function (or propagator) via the self-consistent iteration of a set of non-linear equations. Its first-order approximation, known as $GW$, corresponds to a resummation of ring diagrams and has shown to be extremely successful in physics and chemistry. Systematic improvement is possible, although challenging, via the introduction of vertex corrections. Considering anomalous propagators and an external pairing potential, we derive a new self-consistent set of closed equations equivalent to the famous Hedin equations but having as a first-order approximation the particle-particle (pp) $T$-matrix approximation where one performs a resummation of the ladder diagrams. This pp version of Hedin's equations offers a way to go systematically beyond the $T$-matrix approximation by accounting for low-order pp vertex corrections.
The Bethe–Salpeter equation (BSE) is the key equation in many-body perturbation theory based on Green's functions to access response properties. Within the GW approximation to the exchange-correlation kernel, the BSE has been successfully applied to several finite and infinite systems. However, it also shows some failures, such as underestimated triplet excitation energies, lack of double excitations, ground-state energy instabilities in the dissociation limit, etc. In this work, we study the performance of the BSE within the GW approximation as well as the T-matrix approximation for the excitation energies of the exactly solvable asymmetric Hubbard dimer. This model allows one to study various correlation regimes by varying the on-site Coulomb interaction U as well as the degree of the asymmetry of the system by varying the difference of potential Δv between the two sites. We show that, overall, the GW approximation gives more accurate excitation energies than GT over a wide range of U and Δv. However, the strongly correlated (i.e., large U) regime still remains a challenge.
The subject of the thesis focuses on new approximations studied in a formalism based on a perturbation theory allowing to describe the electronic properties of many-body systems in an approximate way. We excite a system with a small disturbance, by sending light on it or by applying a weak electric field to it, for example and the system "responds" to the disturbance, in the framework of linear response, which means that the response of the system is proportional to the disturbance. The goal is to determine what we call the neutral excitations or bound states of the system, and more particularly the single excitations. These correspond to the transitions from the ground state to an excited state. To do this, we describe in a simplified way the interactions of the particles of a many-body system using an effective interaction that we average over the whole system. The objective of such an approach is to be able to study a system without having to use the exact formalism which consists in diagonalizing the N-body Hamiltonian, which is not possible for systems with more than two particles.
Sujets
Aggregates
Dynamique moléculaire
Density-functional theory
Electronic emission
Nucléaire
Semiclassic
Density Functional Theory
Méthodes ab initio
Dissipative effects
High intensity lasers
Molecules
Monte-Carlo
MBPT
Ionization mechanisms
Greens function methods
Agregats
Oxyde de nickel
Activation neutronique
Nickel oxide
Méthode multiréférence
Fission
Hierarchical model
Energy spectrum
Hubbard model
TDDFT
Modèle de Hubbard
Diffusion
An initio methods
Numbers 3360+q
Mean-field
Lasers intenses
3115ee
Electron correlation
Optical response
Metal clusters
Méchanismes d'ionisation
Chaos
Au-delà du champ moyen
Théorie de la fonctionnelle de la densité
CAO
Corrélations
Coulomb presssure
Damping
Landau damping
Irradiation moléculaire
Coulomb explosion
Electron emission
Neutronic
Agrégats
Metal cluster
Neutronique
Hierarchical method
Effets dissipatifs
Relaxation
Collision frequency
Molecular dynamics
Instability
Nanoplasma
Green's functions
Approximation GW
Atom laser
Green's function
Electron-surface collision
Neutron Induced Activation
Ar environment
Extended time-dependent Hartree-Fock
Electronic properties of metal clusters and organic molecules
Deposition
Time-dependent density-functional theory
Angle-resolved photoelectron spectroscopy
Nuclear
Interactions de photons avec des systèmes libres
Fonction de Green
Molecular irradiation
Embedded metal cluster
Electronic excitation
Environment
Dynamics
Dissipation
Inverse bremsstrahlung collisions
Méthodes des fonctions de Green
3640Cg
Explosion coulombienne
Matrice densité
3620Kd
Clusters
Laser
GW approximation
Matel clusters
Instabilité
Electronic properties of sodium and carbon clusters
Collisional time-dependent Hartree-Fock
Multirefence methods
FOS Physical sciences
Champ-moyen
Corrélation forte
Electric field
Corrélations dynamiques
Deposition dynamics
Correction d'auto-interaction