Nearest-neighbor Coulomb Interaction Research Articles

Quantum self-consistent approach to the charge gap of the quasi-one-dimensional organic conductors

We apply an extended quantum self-consistent method, in which quantum fluctuations are taken into account, to the bosonization Hamiltonian to investigate analytically the charge gap in the quasi-one-dimensional (1D) organic conductors at quarter-filling described by the 1D Hubbard model with dimerization and alternate potential on site. It is shown that either dimerization or alternate potential gives rise to the enhancement of the charge gap. Our results are compared with those of the numerical and the other analytical theories. Our results are also consistent with the experimental data of the actual organic materials when the effect of nearest-neighbor Coulomb interaction is taken into account.

Spin- and charge-polarized states in nanographene ribbons with zigzag edges

Effects of the nearest neighbor Coulomb interaction on nanographene ribbons with zigzag edges are investigated using the extended Hubbard model within the unrestricted Hartree-Fock approximation. The nearest Coulomb interaction stabilizes a novel electronic state with the opposite electric charges separated and localized along both edges, resulting in a finite electric dipole moment pointing from one edge to the other. This charge-polarized state competes with the peculiar spin-polarized state caused by the on-site Coulomb interaction and is stabilized by an external electric field.

Quarter-Filled Extended Hubbard Model at Strong Coupling

We apply a perturbation approach to study the quarter-filled extended Hubbard model at strong coupling limit. An effective Hamiltonian up to sixth order in t/U and t/V (t defines electron hopping, U defines on-site Coulomb interaction, and V defines nearest-neighbor Coulomb interaction) for one-dimensional chains was obtained. The spin-spin correlation functions were involved, which can be obtained after comparing to the ground state energy numerically obtained from the phase diagram.

Pattern of charge ordering in quasi-one-dimensional organic charge-transfer solids

We examine two recently proposed models of charge ordering (CO) in the nominally $\frac{1}{4}$-filled, quasi-one-dimensional (1D) organic charge-transfer solids (CTS). The two models are characterized by site charge density ``cartoons'' $\dots{}1010\dots{}$ and $\dots{}1100\dots{},$ respectively. We use the Peierls-extended Hubbard model to incorporate both electron-electron $(e\ensuremath{-}e)$ and electron-phonon $(e\ensuremath{-}ph)$ interactions. We first compare the results, for the purely electronic Hamiltonian, of exact many-body calculations with those of Hartree-Fock (HF) mean-field theory. We find that HF gives qualitatively and quantitatively incorrect values for the critical nearest-neighbor Coulomb repulsion ${(V}_{c})$ necessary for $\dots{}1010\dots{}$ order to become the ground state. Second, we establish that spin-Peierls order can occur in either the $\dots{}1100\dots{}$ and $\dots{}1010\dots{}$ states and calculate the phase diagram including both on-site and intrasite $e\ensuremath{-}\mathrm{ph}$ interactions. Third, we discuss the expected temperature dependence of the CO and metal-insulator transitions for both $\dots{}1010\dots{}$ and $\dots{}1100\dots{}$ CO states. Finally, we show that experimental observations clearly indicate the $\dots{}1100\dots{}$ CO in the 1:2 anionic CTS and the $(\mathrm{TMTSF}{)}_{2}X$ materials, while the results for $(\mathrm{TMTTF}{)}_{2}X$ with narrower one-electron bandwidths are more ambiguous, likely because the nearest-neighbor Coulomb interaction in these materials is near ${V}_{c}.$

Nearest-neighbor attraction stabilizes staggered currents in the two-dimensional Hubbard model

Using a strong-coupling approach, we show that staggered current vorticity does not obtain in the repulsive two-dimensional Hubbard model for large on-site Coulomb interactions, as in the case of the copper oxide superconductors. This trend also persists even when nearest-neighbor repulsions are present. However, staggered flux ordering emerges when attractive nearest-neighbor Coulomb interactions are included. Such ordering opens a gap along the $(\ensuremath{\pi},0)\ensuremath{-}(0,\ensuremath{\pi})$ direction and persists over a reasonable range of doping.

Charge stripes in the extended Hubbard model with nearest-neighbor Coulomb interaction

Using a strong coupling approach, based on a Cumulant Expansion, we investigate the stripe orders driven by nearest-neighbor Coulomb (NNC) interaction in the Hubbard model. When we consider only local Coulomb repulsion, critical charge fluctuations drive the system towards a phase separation (PS). Such density instability evolves into an incommensurate charge density wave (ICDW) when nonlocal Coulomb interactions are taken into account, similarly to the case when long-range Coulomb forces are considered. In particular, we find a stripe phase with a crossover from diagonal to vertical stripes in the doping region 0.03 ?x? 0.2, similarly to neutron scattering experiments on La 2 - x Sr x CuO 4. Analogous strong dependence in the stripe direction is observed at varying the NNC interaction.

Quantum Monte Carlo simulation of the triangular lattice in the repulsive Hubbard model

The repulsive Hubbard model for the triangular lattice in two dimensions is studied by means of a quantum Monte Carlo simulation in the grand canonical ensemble. Both on-site and nearest neighbor Coulomb interactions are taken into account. The one-electron spectral function A(kω) is shown to gradually develop a gap as the temperature is lowered provided the Hubbard U is larger than the bandwidth. Analysis of the spin and charge structure factors (static correlation functions) shows that, while the charge factor remains featureless, the spin factor develops a strong peak very close to the M′ point (2π/3,0) of the small surface Brillouin zone (corresponding to the three-sublattice model). Implications for the behavior of the 3×3 adlayer structures on fourth-group semiconductor surfaces are briefly commented upon.

Phase diagram of half-doped manganites

The phase diagram of half-doped manganites which may consist of experimentally observed ferromagnetic (FM), A-,C-, and charge-exchange (CE)-type antiferromagnetic (AF) states is obtained in terms of a model which is based on double exchange via degenerate e{sub g} orbitals, the on-site Coulomb interaction (U), and the nearest-neighbor Coulomb interaction (V). We find that, because of the strong spatial anisotropy of the electron hoppings, the on-site Coulomb interaction has different effects on these magnetic order states. As a result, large values of U suppress the FM state and favor the A- and C-type AF states. Moreover, we show that it is the interplay between the on-site and nearest-neighbor Coulomb repulsions that stabilizes the CE phase and results in the charge ordering in the state.

Density-functional study of the evolution of the electronic structure of oligomers of thiophene: Towards a model Hamiltonian

We present density-functional and time-dependent density-functional studies of the ground, ionic, and excited states of a series of oligomers of thiophene. We show that, for the physical properties, the most relevant highest occupied and lowest unoccupied molecular orbitals develop gradually from monomer molecular orbitals into occupied and unoccupied broad bands in the large length limit. We show that band gap and ionization potentials decrease with size, as found experimentally and from empirical calculations. This gives credence to a simple tight-binding model Hamiltonian approach to these systems. We demonstrate that the length dependence of the experimental excitation spectra for both singlet and triplet excitations can be very well explained with an extended Hubbard-like Hamiltonian, with a monomer on-site Coulomb and exchange interaction and a nearest-neighbor Coulomb interaction. We also study the ground and excited-state electronic structures as functions of the torsion angle between the units in a dimer, and find almost equal stabilities for the transoid and cisoid isomers, with a transition energy barrier for isomerization of only 4.3 kcal/mol. Fluctuations in the torsion angle turn out to be very low in energy, and therefore of great importance in describing even the room-temperature properties. At a torsion angle of 90° the hopping integral is switched off for the highest occupied molecular orbital levels because of symmetry, allowing a first-principles estimate of the on-site interaction minus the next-neighbor Coulomb interaction as it enters in a Hubbard-like model Hamiltonian.

PHASE DIAGRAM OF STRIPE ORDER IN THE EXTENDED HUBBARD MODEL

The extended Hubbard model with the nearest-neighbor Coulomb interaction on the square lattice is studied within the mean-field approximation. The stable states for 8×8 sites lattice with the periodic boundary condition and the electron filling n=0.875, as well as for 10×10 lattice and n=0.80, are obtained. For 8×8 lattice where quarter-filled straight stripe is expected because of the long-range Coulomb interaction, the cross stripe phases become stable.

Resonant inelastic X-ray scattering in copper oxides

Momentum dependence of resonant inelastic x-ray scattering (RIXS) in one- (1D) and two-dimensional (2D) copper oxides is examined theoretically. Cu K-edge RIXS spectrum is calculated by using the exact diagonalization techniques on small clusters in 1D and 2D Hubbard models with 1s-core bands. We find that the spectral line shape around the zone boundary is sensitive to the nearest-neighbor Coulomb interaction V. Whereas the anisotropic momentum dependence in the 2D case stressed in the previous work [Phys. Rev. Lett. 80 (1999) 3705] remains irrespective of V.

New type of charge and magnetic order in the ferromagnetic kondo lattice

We study numerically the one dimensional ferromagnetic Kondo lattice, a model widely used to describe nickel and manganese perovskites. By including a nearest-neighbor Coulomb interaction ( V) and a superexchange interaction between the localized moments ( K), we obtain the phase diagram in parameter space for several dopings at T = 0. Because of the competition between double and superexchange, we find a region where the formation of magnetic polarons induces a charge-ordered state which survives also for V = 0. This mechanism should be taken into account in theories of charge ordering involving spin degrees of freedom.

Four-band extended Hubbard Hamiltonian for the one-dimensional cuprateSr2CuO3:Distribution of oxygen holes and its relation to strong intersite Coulomb interaction

We have carried out experimental and theoretical studies of the unoccupied electronic structure of ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3},$ which can be regarded as the best realization of a one-dimensional model system containing cuprate chains. In the polarization-dependent x-ray absorption spectra, the contributions to the upper Hubbard band from states originating from the two inequivalent oxygen sites are energetically well separated. Theoretical analysis of the measured hole distribution within cluster calculations reveals a markedly enhanced effective nearest-neighbor intersite Coulomb interaction, ${V}_{\mathrm{pd}}\ensuremath{\sim}2$ to 3 eV, or sizable contributions from next-nearest-neighbor interactions, provided a finite on-site energy difference of the two inequivalent oxygen sites ${\ensuremath{\Delta}}_{\mathrm{pp}}$ is taken into account. Including next-nearest-neighbor interactions, reasonable agreement can be achieved with recent electron energy-loss spectroscopy data from the same compound. The $2p$ oxygen orbital analysis of the unoccupied electronic structure of the single-chain cuprate ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$ reveals strong similarities with that of the double chain compound ${\mathrm{SrCuO}}_{2}.$

Charge-orbital ordering and phase separation in the two-orbital model for manganites: Roles of Jahn-Teller phononic and Coulombic interactions

The main properties of realistic models for manganites are studied using analytic mean-field approximations and computational numerical methods, focusing on the two-orbital model with electrons interacting through Jahn-Teller (JT) phonons and/or Coulombic repulsions. Analyzing the model including both interactions by the combination of the mean-field approximation and the exact diagonalization method, it is argued that the spin-charge-orbital structure in the insulating phase of the purely JT-phononic model with a large Hund coupling ${J}_{\mathrm{H}}$ is not qualitatively changed by the inclusion of the Coulomb interactions. As an important application of the present mean-field approximation, the CE-type antiferromagnetic state, the charge-stacked structure along the z axis, and ${(3x}^{2}\ensuremath{-}{r}^{2}{)/(3y}^{2}\ensuremath{-}{r}^{2})$-type orbital ordering are successfully reproduced based on the JT-phononic model with large ${J}_{\mathrm{H}}$ for the half-doped manganite, in agreement with recent Monte Carlo simulation results. Topological arguments and the relevance of the Heisenberg exchange among localized ${t}_{2\mathrm{g}}$ spins explains why the inclusion of the nearest-neighbor Coulomb interaction does not destroy the charge stacking structure. It is also verified that the phase-separation tendency is observed both in purely JT-phononic (large ${J}_{\mathrm{H}})$ and purely Coulombic models in the vicinity of the hole undoped region, as long as realistic hopping matrices are used. This highlights the qualitative similarities of both approaches and the relevance of mixed-phase tendencies in the context of manganites. In addition, the rich and complex phase diagram of the two-orbital Coulombic model in one dimension is presented. Our results provide robust evidence that Coulombic and JT-phononic approaches to manganites are not qualitatively different ways to carry out theoretical calculations, but they share a variety of common features.

Critical Temperatures in the Three-Band Extended Hubbard Model

We investigate the three-band extended Hubbard model for the CuO2 planes of high-temperature superconductors. We consider the limit of U = ∞ on Cu atoms and we include the nearest-neighbor Coulomb repulsion between holes on 2px,y orbitals of oxygen and holes on 3d or 3d orbitals of copper (Vx and Vz respectively, with Vx > Vz). This leads to the effective negative nearest-neighbor Coulomb interaction. Numerical analysis of this model reveals the possibility of s-wave and d-wave superconductivity arising from the difference ΔV = Vz — Vx. It was shown that the s-wave superconductivity is driven by ΔV and is opposed by the Coulomb repulsion on oxygen, Up, while the d-wave superconductivity is influenced only by the driving force, ΔV. This fact would enable existence of the d-wave superconductivity in many high temperature superconducting materials.

Theory of Coexistence of Charge-Ordering and Antiferromagnetic Phases in R0.5A0.5MnO3**The project supported by National Natural Science Foundation of China and the Doctoral Programme Foundation of the Institution of Higher Education of China

Based on a model Hamiltonian with the nearest-neighbor Coulomb interaction of the itinerant eg electrons, we investigated the possibility of the coexistence of the charge-ordering phase and the antiferromagnetic phase for the manganites R1-xAxMnO3 with the doping of x = 0.5. Three different types of the magnetic configurations (CE-type antiferromagnetism, simple antiferromagnetism, and ferromagnetism) have been compared by numerical calculation under the mean-field approximation. We found that the charge-ordering phase may coexist with the CE-type antiferromagnetic phase if the nearest-neighbor Coulomb interaction exceeding a certain critical value.

Resonant inelastic x-ray scattering in one-dimensional copper oxides

The Cu K-edge resonant inelastic x-ray scattering (RIXS) spectrum in one-dimensional insulating cuprates is theoretically examined by using the exact diagonalization technique for the extended one-dimensional Hubbard model with nearest neighbor Coulomb interaction. We find the following characteristic features that can be detectable by RIXS experiments: (i) The spectrum with large momentum transfer indicates the formation of excitons, i.e., bound states of holon and doublon. (ii) The spectrum with small momentum transfer depends on the incident photon energy. We propose that the RIXS provides a unique opportunity to study the upper Hubbard band in one-dimensional cuprates.

Calculation of the optical conductivity spectra of one-dimensional quarter-filled molecular conductors on the basis of a mean-field approximation

The optical conductivity spectra of one-dimensional quarter-filled molecular conductors are calculated at T=0 on the basis of the mean-field approximation applied to the extended Hubbard Hamiltonian. The calculated spectra exhibit a remarkable absorption band in the mid-infrared range. The spectral intensity obtained in this approximation is roughly consistent with that evaluated by Mila through the sum rule, except when the exciton formation due to the nearest neighbor Coulomb interaction (V) is dominant. The results are qualitatively consistent with experimental results.

Antiferromagnetic phases of one-dimensional quarter-filled organic conductors

The electronic states of quasi-one-dimensional organic conductors is studied theoretically at absolute zero based on the Hartree approximation. The nearest-neighbor Coulomb interaction introduces charge disproportionation, which can be seen as a Wigner crystal, accompanied by antiferromagnetism.

Curvature of levels and charge stiffness of one-dimensional spinless fermions

Combining the Bethe Ansatz with a functional deviation expansion and using an asymptotic expansion of the Bethe Ansatz equations, we compute the curvature of levels D_n at any filling for the one-dimensional lattice spinless fermion model. We use these results to study the finite temperature charge stiffness D(T). We find that the curvature of the levels obeys, in general, the relation D_n=D_0+\delta D_n, where D_0 is the zero-temperature charge stiffness and \delta D_n arises from excitations. Away from half filling and for the low-energy (gapless) eigenstates, we find that the energy levels are, in general, flux dependent and, therefore, the system behaves as an ideal conductor, with D(T) finite. We show that if gapped excitations are included the low-energy excitations feel an effective flux \Phi^{eff} which is different from what is usually expected. At half filling, we prove, in the strong interacting limit and to order 1/V (V is the nearest-neighbor Coulomb interaction), that the energy levels are flux independent. This leads to a zero value for the curvature of levels D_n and, as consequence, to D(T)=0, proving an earlier conjecture of Zotos and Prelov\v{s}ek.