We investigate two-site electronic correlations within generalized Hubbard model, which incorporates the conventional Hubbard model (parameters: t (hopping between nearest neighbours), U (Coulomb repulsion (attraction))) supplemented by the intersite Coulomb interactions (parameters: J (1) (parallel spins), J (2) (antiparallel spins)) and the hopping of the intrasite Cooper pairs (parameter: V ).As a first step we find the eigenvalues Eα and eigenvectors |E α of the dimer and we represent each partial Hamiltonian Eα|Eα Eα| (α = 1, 2, . . ., 16) in the second quantization with the use of the Hubbard and spin operators.Each dimer energy level possesses its own Hamiltonian describing different two-site interactions which can be active only in the case when the level will be occupied by the electrons.A typical feature is the appearance of two generalized t-J interactions ascribed to two different energy levels which do not vanish even for U = J (1) = J (2) = V = 0 and their coupling constants are equal to ±t in this case.In the large U -limit for J (1) = J (2) = V = 0 there is only one t-J interaction with coupling constant equal to 4t 2 /|U | as in the case of a real lattice.The competition between ferromagnetism, antiferromagnetism and superconductivity (intrasite and intersite pairings) is also a typical feature of the model because it persists in the case U = J (1) = J (2) = V = 0 and t = 0.The same types of the electronic, competitive interactions are scattered between different energy levels and therefore their thermodynamical activities are dependent on the occupation of these levels.It qualitatively explains the origin of the phase diagram of the model.We consider also a real lattice as a set of interacting dimers to show that the competition between magnetism and superconductivity seems to be universal for fermionic lattice models.
We investigate two-site electronic correlations within generalized Hubbard model, which incorporates the conventional Hubbard model (parameters: t (hopping between nearest neighbours), U (Coulomb repulsion (attraction))) supplemented by the intersite Coulomb interactions (parameters: J (1) (parallel spins), J (2) (antiparallel spins)) and the hopping of the intrasite Cooper pairs (parameter: V ).As a first step we find the eigenvalues Eα and eigenvectors |E α of the dimer and we represent each partial Hamiltonian Eα|Eα Eα| (α = 1, 2, . . ., 16) in the second quantization with the use of the Hubbard and spin operators.Each dimer energy level possesses its own Hamiltonian describing different two-site interactions which can be active only in the case when the level will be occupied by the electrons.A typical feature is the appearance of two generalized t-J interactions ascribed to two different energy levels which do not vanish even for U = J (1) = J (2) = V = 0 and their coupling constants are equal to ±t in this case.In the large U -limit for J (1) = J (2) = V = 0 there is only one t-J interaction with coupling constant equal to 4t 2 /|U | as in the case of a real lattice.The competition between ferromagnetism, antiferromagnetism and superconductivity (intrasite and intersite pairings) is also a typical feature of the model because it persists in the case U = J (1) = J (2) = V = 0 and t = 0.The same types of the electronic, competitive interactions are scattered between different energy levels and therefore their thermodynamical activities are dependent on the occupation of these levels.It qualitatively explains the origin of the phase diagram of the model.We consider also a real lattice as a set of interacting dimers to show that the competition between magnetism and superconductivity seems to be universal for fermionic lattice models.
We find the eigenvalues $E_α $ and eigenvectors ∣Eα> of the extended Hubbard dimer and we represent each part Eα∣Eα><Eα∣ of the dimer Hamiltonian (α=1,2,...,16)in the second quantizations with the use of the Hubbard and spin operators. This procedure gives a review of all competitive, intrinsic interactions, deeply hidden in the orginal form of the considered Hamiltonian. Among competitive interactions we can find ferromagnetic and antiferromagnetic interactions (also in the form appearing in the t−J model), hopping of the Cooper pairs between different dimer lattice sites (similar as in Kulik-Pedan, Penson-Kolb models), as well as, intersite Cooper pair interactions. We plot several coupling constants of these interactions vs Coulomb intrasite interaction U to show that the competition between them strongly depends on the model parameters. The thermodynamical activity of each particular interaction, belonging to a given energy level, depends, however, on the occupation of this level. From the presented review of interactions it is evident that the extended Hubbard model is capable to describe the properties of superconductors with magnetic ordering (including also high-TC superconductors) where a strong competition between magnetism and superconductivity takes place.
The description of a solid at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. The Hubbard model used in this research describes interacting electrons in narrow energy bands, with application to problems as diverse as high – Tc superconductivity, band magnetism and the metal-insulator transition. This research seeks to solve one of the most challenging problems in Theoretical physics which is to describe electronic correlations. In this research the t – U Hubbard model is used to solve analytically and numerically using the exact diagonalization techniquesThis research work focused on the spin interaction and magnetic behavior of some systems and it is therefore an investigation into the various phenomena seen in the phase diagram of ferromagnetic systems. We studied the 2 electrons on 2 sites, 2 electrons on 3 sites and 2 electrons on 4 sites all in One-Dimension (1-D), where the onsite coulomb repulsion, U, and the hopping matrix element, t, were varies to determine their magnetic phase diagram.This results obtained shows that, as the values of the onsite coulomb repulsion, U, increases in all the lattice systems studied, the electronic correlation that favours ferromagnetism gets stronger, but there were no clear transition, and at some point the lattices loss its antiferromagnetic properties, hence the instability of ferromagnetism were established. It was also observed that as the hopping matrix element, t, increases the electronic correlation that favours ferromagnetism get stronger and the lattice begins to loss antiferromagnetic properties but beyond the transition point the lattice began to gain a much stronger antiferromagnetism, hence the ferromagnetism is unstable.
The description of a solid at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons.The Hubbard model used in this research describes interacting electrons in narrow energy bands, with application to problems as diverse as high -Tc superconductivity, band magnetism and the metal-insulator transition.This research seeks to solve one of the most challenging problems in Theoretical physics which is to describe electronic correlations.In this research the t -U Hubbard model is used to solve analytically and numerically using the exact diagonalization techniques This research work focused on the spin interaction and magnetic behavior of some systems and it is therefore an investigation into the various phenomena seen in the phase diagram of ferromagnetic systems.We studied the 2 electrons on 2 sites, 2 electrons on 3 sites and 2 electrons on 4 sites all in One-Dimension (1-D), where the onsite coulomb repulsion, U, and the hopping matrix element, t, were varies to determine their magnetic phase diagram.This results obtained shows that, as the values of the onsite coulomb repulsion, U, increases in all the lattice systems studied, the electronic correlation that favours ferromagnetism gets stronger, but there were no clear transition, and at some point the lattices loss its antiferromagnetic properties, hence the instability of ferromagnetism were established.It was also observed that as the hopping matrix element, t, increases the electronic correlation that favours ferromagnetism get stronger and the lattice begins to loss antiferromagnetic properties but beyond the transition point the lattice began to gain a much stronger antiferromagnetism, hence the ferromagnetism is unstable.
We study the effect of the correlated hopping term and the intersite Coulomb interaction term on principal features of the d-wave superconducting (SC) state, in both the electron- and hole-doped regimes within the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model. In our analysis, we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF), which allows us to go beyond the renormalized mean-field theory (RMFT). We show that the correlated hopping term enhances the pairing at the electron-doped side of the phase diagram. Moreover, the so-called non-BCS regime (which manifests itself by the negative kinetic energy gain at the transition to the SC phase) is narrowed down with the increasing magnitude of the correlated hopping $\ensuremath{\sim}K$. Also, the doping dependencies of the nodal Fermi velocity and Fermi momentum, as well as the average number of double occupancies, are analyzed with reference to the experimental data for selected values of the parameter K. For the sake of completeness, the influence of the intersite Coulomb repulsion on the obtained results is provided. Additionally, selected results concerning the Hubbard-model case are also presented. A complete model with all two-site interactions is briefly discussed in Appendix for reference.
Abstract Using the strong coupling diagram technique, we investigate the extended Hubbard model on a two-dimensional square lattice. This approach allows for charge and spin fluctuations and a short-range antiferromagnetic order at nonzero temperatures. The model features the first-order phase transition to states with alternating site occupations (SAO) at the intersite repulsion v = v c . In this work, we show that doping decreases v c . For a nonzero next-nearest neighbor hopping t ′ , less mobile carriers produce a stronger fall in v c . For half-filling and t ′ = 0 , we consider phase diagrams for a fixed temperature T, on-site U, and intersite repulsions. The diagrams contain regions of SAO, Mott insulator, and several metallic states distinguished by their densities of states. Two of them are characterized by a dip and a peak at the Fermi level. The dip originates from the Slater mechanism for itinerant electrons, while the peak to bound states of electrons with localized magnetic moments. The existence of these two metallic regions in the phase diagram is a manifestation of the Pomeranchuk effect. The boundary between these regions reveals itself as a kink in the curve v c (T) and as a maximum in the T dependence of the double occupancy D. Our calculated D for different values of v, U, and T are in semiquantitative agreement with Monte Carlo results.