In this lecture we present many-body perturbation theory as a method to determine quasiparticle excitations in solids, especially electronic band structures, accurately from first principles.The main ingredient is the electronic self-energy that, in principle, contains all many-body exchange and correlation effects beyond the Hartree potential.As its exact mathematical expression is unknown, approximations must be used in practical calculations.The approximation is obtained using a systematic algebraic approach on the basis of Green function techniques.It constitutes an expansion of the self-energy up to linear order in the screened Coulomb potential, which describes the interaction between the quasiparticles and includes dynamic screening through the creation of exchange-correlation holes around the bare particles.The implementation of the approximation relies on a perturbative treatment starting from density functional theory.Besides a detailed mathematical discussion we focus on the underlying physical concepts and show some illustrative applications.
We present the results of a recently developed approach where the interplay between the itinerant and localized character of electrons in narrow band materials is described by adding on-site correlation effects to a first principle band calculation: the single particle band states are treated as mean field solutions of a multi-orbital Hubbard Hamiltonian and the many-body term associated to localized e-e interaction is described in a configuration-interaction scheme. The method allows to calculate hole and electron spectral functions which can be directly compared with spectroscopical results.
Three-body problem involving two valence holes and a single conduction electron, which appears in the study of the final state of the resonant photoemission in insulators and semiconductors, is formulated to be solved exactly in a two-band Hubbard model by use of Faddeev's scattering theory. The wave functions and energy eigenvalues are calculated numerically in a one-dimensional model. By use of this exact solution of the three-body problem, resonance photoemission spectra are studied from a weak correlation resion to a strong one. It is shown that the approximation used in the past analysis, in which two valence holes are assumed to be localized, deviates from the present results even in the strong correlation region U v v ∼2 W v with U v v and W v denoting the Coulomb integral and the band width of valence holes, respectively.
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.
A methodology is introduced for the systematic treatment of electron-electron correlations in solids and other interacting quantum
N-particle systems. The method is developed within the framework of electronic structure theory (band theory) but, in contrast to conventional approaches, which are based on the single-particle picture, it is formulated within a many-particle picture in which
n particles in
d-dimensional phase space are treated as a single particle in a phase space of
nd dimensions. In this phase space, interparticle interactions appear as external potentials allowing the treatment of the system of particles through the use of single-particle methods, while at the same time allowing a systematic, direct, and nonperturbative treatment of interparticle interactions. The method makes use of the invariance of the Hamiltonian describing an interacting-particle system under partitioning into subsystems of
n particles. This treatment leads to exact results in the limit $n\ensuremath{\rightarrow}N$. Based on such partitioning, we propose a generalization of density functional theory and an appropriately defined local density approximation to treat the interactions between the
n-particle units in a system of
N> n particles. This approach yields
n-particle correlated densities and
n-particle states which can be used in an analysis of the electronic properties of materials, such as total energy, phase stability, electronic transport, and others. We use the formal construct of multiple-scattering theory to develop the method for the calculation of the two-particle electronic structure of a solid and the corresponding total energy of the ground state. We also illustrate some of the properties of the method in terms of a Hubbard model Hamiltonian on a linear ring. Various features of the method and further possible applications are presented in a discussion section.
We have studied the role of on-site correlation in the low-energy excitations of
YBa2Cu3O7 in the normal state, calculating self-energies and spectral functions according to the three-body-scattering approach. The method allows to include all the details of realistic ab initio band-structure calculations and to augment them with the inclusion of electron-electron correlations, getting quasiparticle energies for one-particle removal. It is found that correlation effects modify the energy dispersion of hole quasiparticle states, both in the high and low binding energy region, and strongly modify the Fermi surface topology.