With the use of Hartree-Fock method we find that in narrow band solids there may arise an electron phase separation. These electron regions are spontaneously self-organized into the form of linear electron strings or droplets. The many-body self-trapping effect is due to a deformational electron-phonon interaction. A single string in a narrow band solid consists of a continuos chain of atoms which have trapped electrons (holes) due to the self-creation of a deformation well around this chain. We find that the length of such strings depends on the constant of deformation potential, the elastic modulus of the crystal and the inter-site Coulomb interaction between the particles.
With the use of Hartree-Fock method we find that in narrow band solids there may arise an electron phase separation. These electron regions are spontaneously self-organized into the form of linear electron strings or droplets. The many-body self-trapping effect is due to a deformational electron-phonon interaction. A single string in a narrow band solid consists of a continuos chain of atoms which have trapped electrons (holes) due to the self-creation of a deformation well around this chain. We find that the length of such strings depends on the constant of deformation potential, the elastic modulus of the crystal and the inter-site Coulomb interaction between the particles.
We propose a new, alternative method for ab-initio calculations of the electronic structure of solids, which has been specifically adapted to treat many-body effects in a more rigorous way than many existing ab-initio methods. We start from a standard band-structure calculation for an effective one-particle Hamiltonian approximately describing the material of interest. This yields a suitable set of one-particle basis functions, from which well localized Wannier functions can be constructed using a method proposed by Marzari and Vanderbilt. Within this (minimal) basis of localized Wannier functions the matrix elements of the non-interacting (one-particle) Hamiltonian as well as the Coulomb matrix elements can be calculated. The result is a many-body Hamiltonian in second quantization with parameters determined from first principles calculations for the material of interest. The Hamiltonian is in the form of a multi-band Hamiltonian in second quantization (a kind of extended, multi-band Hubbard model) such that all the standard many-body methods can be applied. We explicitly show how this approach can be solved in the simplest many-body approximation, the mean-field Hartree-Fock approximation (HFA), which takes into account exact exchange and corrects for self-interaction effects.
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]
As ones know,the polaron is a quasiparticle formed by an electron and phonons.Due to Coulomb interaction,the electron will make the lattice deformation take place,meanwhile,the deformation potential(induced) by the lattice deformation will exert on the electron,the electron-phonon interaction influence doubtless on the state of motion of an electron,for example,the energy band and effective mass of an electron could change by the interaction,the electron can also be trapped by the deformable lattice,therefore,the research on the(polaron) is very important in understanding optical and transport properties of a solid. Studying electron-phonon interaction has been a main subject in condensed matter physics;in experiments,the influences of the temperature on the forbidden-band width of semiconductors have been observed very early,with the increase of the temperature,the forbidden-band width of most semiconductors will narrow,but a few will widen,these situations are closely relevant to the electron-phonon interaction.In particular,(recently),a large amount of experimental results,ranging from infrared spectroscopy to transport properties(involving) the colossal magnetoresistance and high-T_c superconductivity,has pointed out the importance of the electron-phonon interaction,which has renewed the interest in studying the models of the electron-phonon(coupled) system,especially,the Holstein polaron,for its relative simplicity,is the most considered model for the interaction of a single tight-binding electron coupled to phonons. In the past several decades,the Holstein poloron has been studied in detail in one-dimensional lattices,various theoretical methods,such as variational approaches,the Global-Local variational method,the(coherent)-state expansion method,have been developed to study features of the Holstein polaron including ground-state energy,polaron energy band,effective mass and so on.However,so far,the work considering the influences of the temperature on features of the Holstein polaron is little still. The main aim of this paper is to investigate the influences of the temperature on the energy-band width and the effective mass of the Holstein polaron by using the canonical transformation method.It is shown that,at certain coupling strength,the energy-band width of the Holstein polaron will narrow and the effective mass will augment with the increase of the temperature,in particular,when electron-phonon coupling strength is big enough,the energy-band width will become zero rapidly in small region of temperature,in fact,the situation is rapid transition of the polaron from the energy-band state to the self-trapping local state,this is an(interesting) result obtained in the paper.It is obvious that these features of the Holstein polaron are very useful in explaining optical and transport properties of a solid.
We consider a lattice model in which phonons scatter with pairs of electrons carrying a net spin current. All the energy eigenvalues and eigenvectors of this model can be obtained analytically. For a suitable choice of parameters the ground state consists of a Fermi sea of non-interacting electrons, with a layer of paired electrons on top of it. The binding energy of one electron pair is partly canceled by increased kinetic energy of another pair of electrons. This results in a momentum-dependent gap in the spectrum of the electrons.
Ab initio electron propagator methods are developed to study electronic properties of molecular systems with strong electron-electron and electron-phonon interactions. For the calculation of electron Green's functions we apply a canonical small polaron transformation that intrinsically contains strong electron-phonon effects. In the transformed Hamiltonian, the energy levels for the noninteracting particles are shifted down by the relaxation (solvation) energies. The Coulomb integrals are also renormalized by the electron-phonon interaction. For certain values of the electron-phonon coupling constants, the renormalized Coulomb integrals can be negative which implies the attraction between two electrons. Within the small polaron transformation we develop a diagrammatic technique for the calculation of electron Green's function in which the electron-phonon interaction is already included into the multiple phonon correlation functions. Since the decoupling of the phonon correlation functions is impossible, and therefore, a Wick's theorem for such correlation functions is invalid, there is no Dyson equation for the electron Green's function. To find the electron Green's function, we use different approximations. One of them is a link-cluster approximation that includes diagonal transitions for the renormalized zeroth Green's function. In the linked-cluster approach the Dyson equation is derived in the most general case, where the self-energy operator is an arbitrary functional (not only in the Hartree-Fock approximation). It is shown that even a Hartree-Fock electron (hole) is not a particle any longer. It is a quasiparticle with a finite lifetime that depends on energy of particle and hole states in different ways. As a consequence of this, a standard description of a Hartree-Fock approximation in terms of wave functions becomes inappropriate in this problem. To challenge the linked-cluster approximation we develop a different approach: a sequential propagation approximation where scattering events occur only for sequential transitions. A self-consistent Hartree-Fock equation for a four-index Green's function matrix is derived. In conclusion, the proposed schemes can be considered for future method developments for quantum chemical calculations for large molecules with strong nonadiabatic effects, e-e correlated electron transfer reactions, and electron transport in molecular transport junctions.