Generalized Hubbard Hamiltonian Research Articles

Few correlated particles in the Hubbard model

The ground state binding energy of few particles in an infinite one-dimensional periodic and quasiperiodic lattice is investigated rigorously in a Hubbard-like model, using a real-space method. We studied the three-body problem in the periodic lattice with correlated hoppings, for the case of non-parallel spin in an infinite linear chain, applying the generalized Hubbard Hamiltonian. The correlation is studied for different values of the hopping parameters as well as the on-site and the inter-site interactions. The results show an effect of the frustration of antibonding states on the pairing behavior. In the case of one-dimensional quasiperiodic lattice we give some preliminary results for two electrons with non-parallel spin.

Transition phenomenon inTi2O3using the discrete variationalXαcluster method and periodic shell model

The electronic structure of the metallic ${\mathrm{Ti}}_{2}{\mathrm{O}}_{3}$ and insulating phases has been investigated using a combination of the three-dimensional periodic shell model and the discrete-variational $(\mathrm{DV})\ensuremath{-}X\ensuremath{\alpha}$ cluster method. Besides the effects of intersite repulsive nearest-neighbor electron-electron $(d\ensuremath{-}d)$ Coulombic interaction and the spin-spin interaction by means of a generalized Hubbard Hamiltonian, the Hamiltonian in the insulating phase includes Anderson's attractive potential due to the electron-phonon interaction. The shell model estimates the electron-phonon coupling constants, and provides direct theoretical evidence that the electron-phonon interaction stabilizes the three dimensional periodic distribution of ${\mathrm{Ti}}^{3+}{\mathrm{\ensuremath{-}}\mathrm{Ti}}^{3+}$ pairs along the $c$ axis of the corundum structure. The $\mathrm{DV}\ensuremath{-}X\ensuremath{\alpha}$ cluster method calculates the electron energies in the $[{\mathrm{Ti}}_{2}{\mathrm{O}}_{9}{]}^{\mathrm{\ensuremath{-}}12}$ cluster, the values for the intersite repulsive nearest-neighbor $d\ensuremath{-}d$ interaction, and the spin-spin interaction. The electron correlation effect and the spin correlation effect are found to be mainly responsible for the broad crossover between a metallic and an insulating state in ${\mathrm{Ti}}_{2}{\mathrm{O}}_{3},$ although there is some contribution from the electron-phonon interaction. The present calculation describes the characteristic transition phenomenon in this material.

Three-Body Correlation in the Diluted Generalized Hubbard Model

ABSTRACTA real-space method has been used to solve the generalized Hubbard Hamiltonian for a system with few electrons. The method is based on mapping the correlated many-body problem onto an equivalent tight-binding one in a higher dimensional space. For a linear chain, we have obtained an exact solution of the problem of three non-parallel electrons. The three-body correlation are studied by examining the binding energy in the ground state, for different values of the hopping parameters and of the on-site (U) and nearest-neighbor (V) interactions.

Theoretical Study of Spin Alignment of Organic High-Spin Molecules in Terms of VB Description

Abstract Spin alignment in organic high-spin molecules and their topological isomers with both unpaired π and [sgrave] electrons has been studied by the exact numerical solutions of the valence-bond Heisenberg Hamiltonian and of the UHF calculation of the generalized Hubbard Hamiltonian. In order to clarify the main path-way of the spin correlation, the spin configurations with large coefficients have been extracted from the eigenfunctions in the ground and low-lying excited states of the Heisenberg Hamiltonian. The contributions of their spin configurations to the total spin energy have been calculated. Using this procedure, important spin configurations (important path-way of exchange correlations) of the ground and low-lying excited states have been clarified. A similar treatment can be carried out by the generalized Hubbard Hamiltonian. Thus, the VB decompositions of UHF solutions of the generalized Hubbard model have been carried out using the total α spin and total β spin densities on each carbon si...

Local alkali-metal-promoted oxidation of Si(100)-(2 x 1) surfaces: A generalized-Hubbard-model calculation.

In order to study the local regime in the alkali-metal-promoted oxidation of silicon, we consider the coadsorption of an oxygen molecule and a potassium atom on the dimerized Si(100)-(2\ifmmode\times\else\texttimes\fi{}1) surface. Antiferromagnetic (singlet) spin correlations within the Si dimers are taken into account from the outset by working with a generalized Hubbard Hamiltonian. In this background, the adsorption of a K atom strongly polarizes the medium creating a local charge-spin bag, around the ${\mathrm{K}}^{+}$ ion, which sets the scenario for promoted oxidation. When an ${\mathrm{O}}_{2}$ molecule in its ground state ${(}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}$) approaches this region of the surface, it is influenced by the attractive electrostatic field of the ${\mathrm{K}}^{+}$ ion, with the corresonding lowering of its affinity level. This eventually crosses the Fermi level and captures the excess electron charge in the bag. A superoxide ${\mathrm{O}}_{2}$ ion, the $^{2}\mathrm{\ensuremath{\Pi}}_{\mathit{g}}$ state, is thereby formed, ionicly bonded to ${\mathrm{K}}^{+}$ and covalently bonded to the Si dimer. In the absence of potassium, the oxygen molecule simply physisorbs in a state adiabatically connected to its gas-phase ground state.

Generalized Hubbard Hamiltonian: Renormalization-group approach.

We study a generalized Hubbard Hamiltonian which is closed within the framework of a quantum real-space renormalization group, which replaces the d-dimensional hypercubic lattice by a diamondlike lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled-band case for d=2 and d=3. Some evidence for superconductivity is presented.

Electronic properties of high-Tc superconductors.

We study a generalized Hubbard Hamiltonian which includes the Cu and O orbitals in the ${\mathrm{CuO}}_{2}$ planes of high-${T}_{c}$ superconductors. We use slave-boson technique to account for the intra- and interatomic correlations. In the saddle-point approximation we obtain the metal-insulator phase diagram and conclude that, for one hole per unit cell in the ${\mathrm{CuO}}_{2}$ plane, ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ is a charge-transfer insulator. Our results show that doping produces a rapid metallization of the system and destroys antiferromagnetic order. Transport properties and mechanism for superconductivity are briefly discussed.

PAIRING IN Cu-O SYSTEMS: RENORMALIZATION GROUP AND EXACT DIAGONALIZATION RESULTS

We model the Cu-O high T c compounds by a generalized Hubbard Hamiltonian that includes an intersite Coulomb repulsion G. We use a real space renormalization group approach to calculate effective interactions and gap energies in infinite chains. The results indicate attraction between added holes in these systems. The magnitudes of these attractive energies are compared with exact results obtained by the Lanczos method for finite clusters.

Correlation effects in the electronic structure of high T c superconductors

We model Cu-O high T c superconductors by a generalized Hubbard Hamiltonian. We obtain the ground state for finite linear chain systems exactly. This allows us to calculate physical quantities to show that: a) those systems can change from a highly ionic to a highly metallic state as holes are added. b) In the metallic state holes tend to form pairs in next nearest neighbour sites.

Spin alignment in organic high-spin molecules as studied by ESR and the generalized Hubbard Hamiltonian approach

In order to examine the role of topological symmetry in spin alignment of organic high-spin molecules, a novel hydrocarbon, 3,4′-diphenylmethylenebis(phenylmethylene) (3,4′-DPBPM), has beeen synthesized and characterized by single-crystal ESR. This molecule has a triplet ground state with a closely located quintet excited state in contrast to its topological isomer, 3,3′-DPBPM, with a non-degenerate septet ground state. UHF SCF calculation of the generalized Hubbard Hamiltonian satisfactorily predicts these results.

Ground-state properties and neutral-to-ionic transformation of organic mixed-stack compounds: Mean-field approximation.

A one-dimensional chain of alternating donor and acceptor molecules has been modeled by a generalized Hubbard Hamiltonian which includes the long-range Coulomb interaction and a coupling of the electronic system to the lattice. The ground-state properties such as charge-density waves centered on the molecules and lattice dimerization have been analyzed. We show that the isostructural neutral-to-ionic phase transition will be discontinuous according to our model. In a system characterized by a large transfer integral a dimerized chain can be stable in a narrow range of balance between the on-site potential and the intersite Coulomb interaction; it suggests the possibility of a reentrant structural phase transition. A qualitative analysis of the model indicates that the traditional Peierls mechanism of dimerization becomes uneffective for a system characterized by a small transfer integral. An alternative approach to the neutral-to-ionic transformation is briefly outlined.

Magnetic Phases of Strongly Correlated Electrons in a Nearly Half‐Filled Narrow Band

AbstractA canonical perturbation technique is used to investigate a nearly half‐filled nondegenerate generalized Hubbard Hamiltonian a t the strong intraatomic correlation limit. Quasiparticle state and the total energy for various magnetic orderings are obtained using the Green function method with the moment‐conserving decoupling scheme. A ground state magnetic phase diagram with antiferromagnetic, ferromagnetic, and mixed phases is derived and compared to existing results. The dependence of the critical W/U ratio for metal‐nonmetal transition on the interatomic exchange is estimated.