In this work we discuss the influence of electronic correlation in finite and extended systems. In particular we stress the fact that the electronic correlation renormalizes the particle-particle interaction in a characteristic way and interpolate these ideas, well-known for extended systems, to small systems. We also sketch briefly how the thermodynamics and critical phenomena in finite systems may be treated.
In this work we discuss the influence of electronic correlation in finite and extended systems. In particular we stress the fact that the electronic correlation renormalizes the particle-particle interaction in a characteristic way and interpolate these ideas, well-known for extended systems, to small systems. We also sketch briefly how the thermodynamics and critical phenomena in finite systems may be treated.
An up-to-date selection of applications of correlation spectroscopy, in particular as far as the mapping of properties of correlated many-body systems is concerned. The book starts with a qualitative analysis of the outcome of the two-particle correlation spectroscopy of localized and delocalized electronic systems as they occur in atoms and solids. The second chapter addresses how spin-dependent interactions can be imaged by means of correlation spectroscopy, both in spin-polarized and extended systems. A further chapter discusses possible pathways for the production of interacting two-particle continuum states. After presenting some established ways of quantifying electronic correlations and pointing out the relationship to correlation spectroscopy, the author addresses in a separate chapter the electron-electron interaction in extended systems, and illustrates the ideas by some applications to fullerenes and metal clusters. The last two chapters are devoted to the investigation of the potential of two-particle spectroscopy in studying ordered surfaces and disordered samples. Throughout the book the material is analyzed using rather qualitative arguments, and the results of more sophisticated theories serve the purpose of endorsing the suggested physical scenarios. The foundations of some of these theories have been presented in a corresponding volume entitled "Concepts of Highly Excited Electronic Systems" (3-527-40335-3).
An up-to-date selection of applications of correlation spectroscopy, in particular as far as the mapping of properties of correlated many-body systems is concerned. The book starts with a qualitative analysis of the outcome of the two-particle correlation spectroscopy of localized and delocalized electronic systems as they occur in atoms and solids. The second chapter addresses how spin-dependent interactions can be imaged by means of correlation spectroscopy, both in spin-polarized and extended systems. A further chapter discusses possible pathways for the production of interacting two-partic
Abstract We have seen that disordered systems give rise to a host of interesting effects related to the localization of states. Thus, from the outset we have explicitly to take account of the localization in the theoretical framework, which makes computer experiments on finite systems an important first-principles method. This situation immediately poses several essential questions, such as: (i) how can the properties of macroscopic systems be deduced from the results for finite systems; and (ii) how can the concept of Anderson localization be extended to disordered systems with electron-electron interactions in a numerical model in which disorder and electron correlation are treated on an equal footing? In this chapter we address these questions. In this section we introduce the concept of renormalization for disordered systems. Specifically, we examine real-space renormalization schemes.
In this work we investigate some aspects of the physics of strongly correlated systems by taking into account both electron-electron and electron-phonon interactions as basic mechanisms for reproducing electronic correlations in real materials. The relevance of the electron-electron interactions is discussed in the first part of this thesis in the framework of a self-consistent theoretical approach, named Composite Operator Method (COM), which accounts for the relevant quasi-particle excitations in terms of a set of composite operators that appear as a result of the modification imposed by the interactions on the canonical electronic fields. We show that the COM allows the calculation of all the relevant Green’s and correlation functions in terms of a number of unknown internal parameters to be determined self-consistently. Therefore, depending on the balance between unknown parameters and self-consistent equations, exact and approximate solutions can be obtained. By way of example, we discuss the application of the COM to the extended t-U- J-h model in the atomic limit, and to the two-dimensional single-band Hubbard model. In the former case, we show that the COM provides the exact solution of the model in one dimension. We study the effects of electronic correlations as responsible for the formation of a plethora of different charge and/or spin orderings. We report the phase diagram of the model, as well as a detailed analysis of both zero and finite temperature single-particle and thermodynamic properties. As far as the single-band Hubbard model is concerned, we illustrate an approximated selfconsistent scheme based on the choice of a two-field basis. We report a detailed analysis of many unconventional features that arise in single-particle properties, thermodynamics and system’s response functions. We emphasize that the accuracy of the COM in describing the effects of electronic correlations strongly relies on the choice of the basis, paving the way for possible multi-pole extensions to the twofield theory. To this purpose, we also study a three-field approach to the single-band Hubbard model, showing a significant step forward in the agreements with numerical data with respect to the two-pole results. The role of the electron-phonon interaction in the physics of strongly correlated systems is discussed in the second part of this thesis. We show that in highly polarizable lattices the competition between unscreened Coulomb and Fröhlich interactions results in a short-range polaronic exchange term Jp that favours the formation of local and light pairs of bosonic nature, named bipolarons, which condense with a critical temperature well in excess of hundred kelvins. These findings, discussed in the framework of the so-called polaronic t-Jp model, are further investigated in the presence of a finite on-site potential ~U , coming from the competition between on-site Coulomb and Fröhlich interactions. We discuss the role of ~U as the driving parameter for a small-to-large bipolaron transition, providing a possible explanation of the BEC-BCS crossover in terms of the properties of the bipolaronic ground state. Finally, we show that a hard-core bipolarons gas, studied as a charged Bose-Fermi mixture, allows for the description of many non Fermi liquid behaviours, allowing also for a microscopic explanation of pseudogap features in terms of a thermal-induced recombination of polarons and bipolarons, without any assumption on preexisting order or broken symmetries. [edited by Author]
Real knowledge is to know the extent of one's ignorance. Confucius, 500 BCE Summary The topic of this chapter is a small selection of the vast array of experimentally observed phenomena chosen to exemplify crucial roles played by the electron– electron interaction. Examples in the present chapter bring out the effects of correlation in ground and excited states as well as in thermal equilibrium. These raise challenges for theory and quantitative many-body methods in treating interacting electrons, the topics of the following chapters. The title of this book is Interacting Electrons . Of course, there are no non-interacting electrons: in any system with more than one electron, the electron–electron interaction affects the energy and leads to correlation between the electrons. All first-principles theories deal with the electron–electron interaction in some way, but often they treat the electrons as independent fermions in a static mean-field potential that contains interaction effects approximately. As described in Ch. 4, the Hartree–Fock method is a variational approximation with a wavefunction for fermions that are uncorrelated, except for the requirement of antisymmetry. The Kohn–Sham approach to DFT defines an auxiliary system of independent fermions that is chosen to reproduce the ground-state density. It is exact in principle and remarkably successful in practice. However, many properties such as excitation energies are not supposed to be taken directly from the Kohn–Sham equations, even in principle. Various other methods attempt to incorporate some effect of correlation in the choice of the potential. This chapter is designed to highlight a few examples of experimentally observed phenomena that demonstrate qualitative consequences of electron–electron interactions beyond independent-particle approximations. Some examples illustrate effects that cannot be accounted for in any theory where electrons are considered as independent particles. Others are direct experimental measurements of correlation functions that would vanish if the electrons were independent. In yet other cases, a phenomenon can be explained in terms of independent particles in some effective potential, but it is deeply unsatisfying if one has to invent a different potential for every case, even for different properties in the same material. A satisfactory theory ultimately requires us to confront the problem of interacting, correlated electrons.
The electronic and magnetic correlations in diatomic molecules are studied rigorously on the basis of a Hubbard Hamiltonian. The problem is treated in three phases separately, firstly for electrons with nondegenerate orbitals, then for electrons with degenerate orbitals, and finally for a mixture of both. In this last case special emphasis is put on the interaction between the electrons in the nondegenerate orbital levels with those in the degenerate orbital levels. In this context some qualitative features of how electronic correlations influence the cohesive forces are sketched. We highlight the extent to which various factors such as the total number of electrons in the system, the Pauli principle, Hund's rule, the level splitting, and the relative size of the transfer integrals are influential in determining the ground-state configurations. Some simple physical guidelines are provided for accurately guessing the various possible ground-state configurations.