Multiband Hubbard Model Research Articles

Local-density functional and on-site correlations: The electronic structure of La2CuO4 and LaCuO3.

State-of-the-art electronic-structure calculations based on the local-density approximation (LDA) to the density functional fail to reproduce the insulating antiferromagnetic ground state in the parent compounds of the high-temperature oxide superconductors. Similar problems have been observed earlier in classical transition-metal oxides such as FeO, CoO, and NiO. In this work we present the method which delivers the correct insulating antiferromagnetic ground state in the correlated oxides preserving other properties as well as the efficiency of the standard LDA. The method embeds the relevant (for a given system of electrons) part of the Hubbard Hamiltonian into the Kohn-Sham LDA equation. The resulting Hamiltonian attempts to fix two intrinsic problems of the LDA: the deficiency in forming localized (atomiclike) moments and the lack of discontinuity of the effective one-particle potential when going from occupied to unoccupied states. We present the detailed study of La2CuO4 and LaCuO3. In the case of La2CuO4 the energy gap and the value of the localized magnetic moment in the stable insulating antiferromagnetic solution are in good agreement with experiment. We compare our results with the standard local spin density approximation calculation and multiband Hubbard model calculations, as well as with results of spectroscopy: inverse photoemission, valence photoemission, and x-ray absorption at the K edge of oxygen. In the case of LaCuO3 such an extensive comparison is limited due to the limited data available for this compound. We discuss, however, the electric and magnetic properties and the insulator-metal-insulator transitions upon increase of oxygen deficiency.

Covalency-driven unusual metal-insulator transition in nickelates.

Electronic structures of metallic ${\mathrm{LaNiO}}_{3}$ and insulating ${\mathrm{NdNiO}}_{3}$ are investigated using electron spectroscopies as well as band-structure and model-Hamiltonian calculations. It is shown that there is an increase in the transfer integral, ${\mathit{t}}_{\mathit{p}\mathit{d}}$ in ${\mathrm{LaNiO}}_{3}$ compared to ${\mathrm{NdNiO}}_{3}$ though ${\mathit{U}}_{\mathit{d}\mathit{d}}$ and \ensuremath{\Delta} are very similar. A phase diagram obtained with a multiband Hubbard model explains the metal-insulator transition as well as the anomalous resistivity of ${\mathrm{NdNiO}}_{3}$ under pressure while indicating various interesting possibilities near the metal-insulator phase line.

Itinerant ferromagnetism of the multiband Hubbard model

We present some exact studies on the ferromagnetic ground state of the multiband Hubbard models including the periodic Anderson model (two-band) and CuO 2 plane in the oxide superconductors (three band). First we show rigorous arguments that the ground state of the periodic Anderson model contains a ferromagnetic phase with spin angular momentum S=(N−1)/2 for Ne=N+1 where N is the number of lattice sites and Ne is that of electrons. Secondly the exact diagonalization technique is applied to small clusters. The models have the phase with high-spin state, indicating that a conduction electron is moving in the ferromagnetic background of localized spins.

Ferromagnetic spin-wave theory in the multiband Hubbard model having a flat band.

The peculiar effect of electron correlation in multiband systems is illustrated for the recently proposed ferromagnetism in a Hubbard model having flat bands. Depsite the flatness of the band, an acoustic spin-wave mode with a finite stiffness exists along with optical modes below a Stoner gap. The relevant energy (gap and stiffness) transmutes from the Hubbard U in the weak-coupling limit to t (transfer integral) in the strong-coupling limit. This implies a stable itinerant ferromagnetism with finite band widths.

THE NATURE OF THE IN-GAP STATES IN WEAKLY DOPED La2−x Srx CuO4

A single-particle density of states is calculated in the strong electron correlation limit of the generalized multiband Hubbard model by exact diagonalization for CuO4 cluster. Several in-gap states are induced by hole doping that are mixtures of Cu d(x2−y2) and b1 O states and Cu d(z2), O a1 states and nonbonding O states. The Fermi level depends on the hole concentration nonmonotonically. The critical concentration of the insulator-metal transition of the Anderson type is estimated.

Exact ground state of a double-layer multiband Hubbard model

An exact result is obtained for the ground state of a quasi-two-dimensional strongly correlated fermion model consisting of two coupled ${\mathrm{CuO}}_{2}$ layers with two orbitals per copper site and one orbital per oxygen site.

Random-phase-approximation approach to optical and magnetic excitations in the two-dimensional multiband Hubbard model.

As a convenient qualitative approach to strongly correlated electronic systems, an inhomogeneous Hartree-Fock plus random-phase approximation is applied to response functions for the two-dimensional multiband Hubbard model for cuprate superconductors. A comparison of the results with those obtained by exact diagonalization by Wagner, Hanke, and Scalapino [Phys. Rev. B 43, 10 517 (1991)] shows that overall structures in optical and magnetic particle-hole excitation spectra are well reproduced by this method. This approach is computationally simple, retains conceptual clarity, and can be calibrated by comparison with exact results on small systems. Most importantly, it is easily extended to larger systems and straightforward to incorporate additional terms in the Hamiltonian, such as electron-phonon interactions, which may play a crucial role in high-temperature superconductivity.

Role of Off-site Interactions in Auger Lineshape Analysis from Closed Bands Systems

The Cini–Sawatzky theory Auger CVV line shapes from solids and its extensions are based on single or multi-band Hubbard or Anderson models, retaining only the intra-atomic repulsion terms. In this work, we study the role of off-site interactions in closed bands systems. The local interaction terms are treated exactly, as usual, while off-site correlations are intorduced as a self-energy-like correction, on perturbative grounds. Our main result is that the effect of off-site interactions must be taken into account to obtain simultaneous agreement for the shape and the energy position of the CVV spectra. This conclusion is supported by recent experimental evidence and affects the derivation of U values from line shape analysis.

Optical and single-particle excitations in the multiband Hubbard model for cuprate superconductors

On the basis of exact diagonalizations a comparative study of optical (two-particle) and single-particle excitations is presented for a 2-D multiorbital Hubbard model. The single-particle excitations display strongly correlated states related to the Zhang-Rice Cu-O singlet construction. These states define the gap (to the upper Hubbard band) at half-filling and become partially occupied by doping holes in our 2 × 2 unit cell system. At a hole concentration δ = 0.25 the imaginary part of the self energy does not vanish close to the Fermi energy, indicating a non-Fermi liquid behavior of the Zhang-Rice states. The optical results show three allowed optical transitions in the low-energy regime: (i) The Drude peak at ω = 0 with spectral weight proportional to z; (ii) a small structure due to transitions within the singlet band complex, which may be related to the experimentally observed midinfrared absorption. Both transitions (i) and (ii) stem from itinerant motion of the Zhang-Rice singlets. (iii) Unbinding of the O hole from the Cu spin in the singlet. This gives a strong absorption peak due to non-bonding oxygen → CuO singlet transitions, again with relative weight ≈ z.

Derivation of a one-band Hubbard model for CuO planar materials.

We have performed numerical studies of multiband Hubbard models for the Cu-O planes of the high-${\mathit{T}}_{\mathit{c}}$ materials. For the range of realistic parameters, all low-energy (\ensuremath{\le}2 eV) charge and spin excitations are described by the single-band (possibly extended) Hubbard model with U\ensuremath{\simeq}W, where W is the bandwidth.

Ferromagnetism in the Hubbard model on line graphs and further considerations

Let L(G) be the line graph of a graph G=(V,E). The Hubbard model on L(G) has ferromagnetic ground states with a saturated spin if the interaction is repulsive (U>0) and if the number of electrons N satisfies N>or=M. M= mod E mod + mod V mod -1 if G is bipartite and M= mod E mod + mod V mod otherwise. The author shows that the ferromagnetic ground state is unique if N=M. Further he gives a sufficient condition for the existence of other ground states if N>M. The results are valid also for a multi-band Hubbard model on a bipartite graph. In the case of a periodic lattice, the results are related to the existence of a flat energy band.

Optical, magnetic, and single-particle excitations in the multiband Hubbard model for cuprate superconductors.

On the basis of exact diagonalizations, a comparative study of two-particle optical and magnetic, as well as single-particle, excitations is presented for a two-dimensional (2D) multiorbital Hubbard model. For reasonable parameter sets appropriate for the cuprate superconductors, the single-particle excitations display strongly correlated states related to the Zhang-Rice Cu-O singlet construction. These states define the gap (to the upper Hubbard band) at half-filling and become partially occupied by doping holes in our 2\ifmmode\times\else\texttimes\fi{}2 unit-cell system. The optical results, which are the first quantitative calculations performed for realistic parameters of the three-band Hubbard model, clearly show three allowed optical transitions: (i) itinerant motion of the Cu-O singlets, having (for doping concentrations x\ensuremath{\ne}0) a spectral Drude distribution around \ensuremath{\omega}=0 with spectral weight proportional to x; (ii) unbinding of the O hole from the Cu spin in the singlet. This gives, in particular, a strong absorption peak due to singlet\ensuremath{\rightarrow}nonbonding oxygen transitions, again with relative weight \ensuremath{\sim}x.It is roughly centered at \ensuremath{\omega}\ensuremath{\sim}${\mathit{J}}_{\mathrm{Kondo}}$, where ${\mathit{J}}_{\mathrm{Kondo}}$ is the Kondo coupling and \ensuremath{\Delta} the bare Cu-O charge-transfer energy. It is this singlet unbinding that results in the by far dominant absorption structure between Drude and higher-energy Cu-O transitions and not the often discussed ``mid-infrared'' absorption due to transitions between different singlet states. (iii) Cu-O charge-transfer processes at energy \ensuremath{\sim}\ensuremath{\Delta}+${\mathit{U}}_{\mathit{p}\mathit{d}}$. They show a pronounced excitonic effect due to the p-d interaction ${\mathit{U}}_{\mathit{p}\mathit{d}}$ and have a reduced spectral weight shifted to higher energies for increased dopings. Findings (i)--(iii) are in general accordance with recent experimental data. Our study of the low-energy absorption is complemented with a numerical scaling analysis of the Drude weight in 1D, where, in particular, we find an interesting violation of Lenz's law for 4n-site Hubbard rings. Finally, the magnetic structure factor is calculated for the 2D case. For finite doping it contains a peak at 2${\mathit{J}}_{\mathrm{Kondo}}$, which should be detectable in experiment.

Erratum: Repulsion-induced superconductivity in a multiband Hubbard model

Erratum: Repulsion-induced superconductivity in a multiband Hubbard model

HUBCOM: A program for Monte Carlo simulations on generalized Hubbard models

We present here a program for performing Monte Carlo (MC) simulations in discrete fermionic systems. We use a special version of the so-called determinantal method. The algorithm is based in the standard Metropolis method, but makes use of a non-uniform probability distribution for the selection of the transition-candidate states. Detailed balance is preserved by suitably modifying the Metropolis acceptance-rejection test. The method was originally developed and used in a one-dimensional spinless fermion model. We apply it to the case of a two-dimensional multi-band Hubbard model. The program code is self-contained and optimized for use in vectorial computers.

Charge-transfer and magnetic-pairing mechanisms in the extended Hubbard model of high-Tc oxides.

Charge-transfer and spin-interaction-mediated pairing is derived within a strong-coupling expansion for an extended multiband Hubbard model describing Cu-O\char21{}based superconductors. We include both intrasite (${\mathit{U}}_{\mathit{d}}$,${\mathit{U}}_{\mathit{p}}$) and intersite (${\mathit{U}}_{\mathit{p}\mathit{d}}$) Coulomb repulsions. The basic carriers are oxygen-hole quasiparticles in ${\mathit{p}}_{\mathrm{\ensuremath{\sigma}}}$ orbitals. They interact via a charge-transfer mechanism driven by ${\mathit{U}}_{\mathit{p}\mathit{d}}$ and via a magnetic mechanism, which is due to a constructive interplay between the enhanced (by ${\mathit{U}}_{\mathit{p}\mathit{d}}$) Kondo (Cu-O) exchange and the superexchange of the Cu spins. Within the BCS limit we find that ${\mathit{U}}_{\mathit{p}\mathit{d}}$ enhances the relative weight of s versus d-wave pairing, with the dominance of s-wave pairing for large transfer energies \ensuremath{\Delta}=${\mathit{E}}_{\mathit{p}}$-${\mathit{E}}_{\mathit{d}}$ and at low-to-intermediate doping. The charge-transfer-induced coupling is negligible in this large-\ensuremath{\Delta} limit. In the small-\ensuremath{\Delta} limit it induces a 10\char21{}20 % enhancement of the BCS ${\mathit{T}}_{\mathit{c}}$.

Three-band Hubbard model: A Monte Carlo study.

We have studied a two-dimensional multiband Hubbard model describing ${\mathrm{CuO}}_{2}$ sheets in the high-${\mathit{T}}_{\mathit{c}}$ oxides. The simulations were performed for a grand-canonical ensemble on lattice sizes up to 16 unit cells of three atoms each and temperatures down to ${\mathit{k}}_{\mathit{B}}$T\ensuremath{\sim}t/30, where t is the Cu-O hybridization. For generally accepted values of the Hubbard coupling on the Cu sites ${\mathit{U}}_{\mathit{d}}$\ensuremath{\gtrsim}6t, two different regimes can be distinguished in the magnetic properties of the model. In the half-filled band case we see for \ensuremath{\Delta}g${\mathit{U}}_{\mathit{d}}$/2 (\ensuremath{\Delta}=${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{p}}$-${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{d}}$ being the charge-transfer energy) the formation of a correlation gap, as expected for a charge-transfer insulator. For \ensuremath{\Delta}${\mathit{U}}_{\mathit{d}}$/2, on the other hand, no gap is visible in the considered temperature region. In this (mixed-valence) situation only a very weak dependence of the magnetic structure form factor on doping is obtained, in contrast to the charge-transfer situation, where a strong decrease of the same quantity is observed for very low concentrations of dopant holes (\ensuremath{\delta}\ensuremath{\lesssim}0.05). The existence of antiferromagnetic long-range order in the two different parameter regions is studied with finite-size scaling in the low-temperature regime. We also investigated the possibility of singlet formation between O holes and the Cu hole on one plaquette, as suggested by Zhang and Rice. The amplitude squared of such a singlet increases strongly as a function of doping, reaching saturation at \ensuremath{\delta}\ensuremath{\simeq}0.2. Finally, we find evidence for an attractive pairing interaction only in the extended s-wave channel for \ensuremath{\delta}=0.2 and \ensuremath{\beta}\ensuremath{\gtrsim}4/t, although no phase transition to a superconducting state could be seen.

Antiferromagnetism of CuO2 layers within a slave-boson approach.

The antiferromagnetic ground state of ${\mathrm{CuO}}_{2}$ layers is studied at the mean-field level within a slave-boson approach to a multiband Hubbard model which includes the ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ orbital for Cu and the ${\mathit{p}}_{\mathit{x}}$ and ${\mathit{p}}_{\mathit{y}}$ orbitals for O. The stability of the antiferromagnetism is tested by varying the separation \ensuremath{\Delta} between p- and d-hole energy levels and by allowing direct O-O hopping. Results for the effective exchange integral, the antiferromagnetic gap, the percentage of d character of holes at the Fermi level, and the Cu magnetic moment are discussed by varying \ensuremath{\Delta}.

Generalized magnetic susceptibilities of itinerant magnetic systems

We use a multiband Hubbard model with intra-atomic Coulomb and exchange interactions for a microscopic description of the magnetic and nonmagnetic properties of fcc iron. High- and low-spin states are calculated by using a simplified version of the fixed-spin-moment (FSM) method of Moruzzi et al., Phys. Rev. B 34 (1986) 1784. We find that the wave-vector dependent spin susceptibility of the high-spin state differs remarkably from the susceptibility of the low-spin state.

Repulsion-induced superconductivity in a multiband Hubbard model.

A multiband Hubbard Hamiltonian (close to the one used to describe CuO{sub 2} planes) is studied with strong-coupling perturbation theory. Two charge-fluctuation mechanisms are described and lead to a spin-independent attraction, which is much larger than the antiferromagnetic interaction. It provides a convincing argument for the possibility of superconductivity induced by repulsive interactions.

Superconducting pairing of the extended multiband Hubbard model: A weak-coupling study.

Pairing mediated by charge and spin fluctuations is examined within the weak-coupling approximation for a three-band Hubbard model for the cuparate superconductors with both intrasite ({ital U}{sub {ital d}},{ital U}{sub {ital p}}) and intersite repulsion ({ital U}{sub {ital pd}}). Like in the one-band situation, paramagnon exchange near a spin-density-wave instability gives rise to a singlet {ital d}-wave pairing interaction. On the other hand, the exchange of charge-fluctuation modes due to {ital U}{sub {ital pd}} leads to {ital s}-wave coupling near an interband instability and to {ital d}-wave coupling near the intraband charge-density-wave instability. When simultaneously on-site interactions are included the {ital s}-wave pairing is shifted to large dopings away from half-filling and again replaced by {ital d}-wave coupling for smaller dopings.