On-top conditional correlation functions of many-electron theory are rearranged into a set of correlon quasiparticles representing the local effect of electron correlation in the ground and excited states. An individual correlon is characterized with a one-particle wave function, the imaginary part of which (or covalent correlon) gives the amplitude of the on-top depletion of the (conditional electron) charge (ODC) due to (strong) electron correlation. In its turn, the real part (ionic correlon) gives the amplitude of the on-top accumulation of the (electron) charge (OAC) due to the ionic squeezing of electrons. The proposed correlon theory is applied to analyze the local correlation effects in the ground and first excited states of the hydrogen molecule as well as of the equidistant and alternate linear hydrogen chains from ${\mathrm{H}}_{4}$ to ${\mathrm{H}}_{12}$. The covalent and ionic correlons obtained at the multiconfigurational self-consistent-field level of correlated functions are demonstrated to be the robust descriptors of the covalency of the ground and the ionicity of the excited ${\mathrm{H}}_{n}$ states.
On-top conditional correlation functions of many-electron theory are rearranged into a set of correlon quasiparticles representing the local effect of electron correlation in the ground and excited states. An individual correlon is characterized with a one-particle wave function, the imaginary part of which (or covalent correlon) gives the amplitude of the on-top depletion of the (conditional electron) charge (ODC) due to (strong) electron correlation. In its turn, the real part (ionic correlon) gives the amplitude of the on-top accumulation of the (electron) charge (OAC) due to the ionic squeezing of electrons. The proposed correlon theory is applied to analyze the local correlation effects in the ground and first excited states of the hydrogen molecule as well as of the equidistant and alternate linear hydrogen chains from H4 to H12. The covalent and ionic correlons obtained at the multiconfigurational self-consistent-field level of correlated functions are demonstrated to be the robust descriptors of the covalency of the ground and the ionicity of the excited Hn states.
This paper presents a general method to describe and analyze electron correlation effects in local-orbital electronic structure calculations using a generalized Hubbard Hamiltonian. In our approach, we first introduce a local density formalism where the total energy of the system is obtained as a function of the orbital occupancies ni associated with each local orbital; in particular, exchange and correlation local potentials are presented for a multilevel case. In parallel, using the dynamical mean field approximation, a many-body solution is obtained by means of a local self-energy that appropriately interpolates between the low and high correlation limits. We also show that the local density and the many-body solutions are linked through charge consistency conditions. These two solutions are applied to a multilevel Anderson impurity and to a multiband Hubbard lattice, our results showing the high accuracy of the approach presented in this paper. Further on, we discuss how to apply our previous analysis to the case of crystals and molecules and analyze several examples: bulk Si, and HF and H2O molecules. The good results obtained for these cases show that our approach for the description of correlation effects offers an interesting alternative to the well-established density functional methods based on the calculation of the electron density $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{r}).$
Abstract We analyze two-particle binding factors of H2, LiH, and HeH+ molecules/ions with the help of our original exact diagonalization ab initio approach. The interelectronic correlations are taken into account rigorously within the second quantization scheme for restricted basis of renormalized single-particle wave functions, i.e., with their size readjusted in the correlated state. This allows us to determine the many-particle covalency and ionicity factors in a natural and intuitive manner in terms of the microscopic single-particle and interaction parameters, also determined within our method. We discuss the limitations of those basic characteristics and introduce the concept of atomicity, corresponding to the Mott and Hubbard criterion concerning localization threshold in many-particle systems. This addition introduces an atomic ingredient into the electron states and thus removes a spurious behavior of covalency with the increasing interatomic distance, as well as provides a more complete physical interpretation of bonding.
With the eigenfunctional theory, we study a general interacting electron system, and give a rigorous expression of its ground state energy, which is composed of two parts: one part is contributed by the non-interacting electrons, and the other one is represented by the correlation functions that are controlled by the electron correlation. Moreover, according to the rigorous expression of the ground state energy, an effective scheme beyond the local density approximation of the density functional theory is proposed. As a simple example for a spin-1/2 XXZ chain, under the linear approximation in solving the equation of the phase field, the ground state energy obtained by the present scheme is quite close to that of the Bethe ansatz.
With the eigenfunctional theory, we study a general interacting electron system, and give a rigorous expression of its ground state energy which is composed of two parts, one part is contributed by the non-interacting electrons, and another one is represented by the correlation functions that are controlled by the electron correlation. Moreover, according to the rigorous expression of the ground state energy, an effective method beyond the local density approximation of the density functional theory is proposed.
We apply our new method of approach to electronic states in correlated systems [for a brief review, Part I, see: Acta Phys. Pol. B31, 2879 (2000)] to the analysis of the states and electron localization in nanoscopic chains containing up to N = 12 atoms. The Mott and the Hubbard criteria of localization are explicitly evaluated and the importance of the former is stressed. We also define the many-particle wave function and calculate it explicitly for the hydrogen molecule. Further applications of our method are listed at the end.
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]