Hubbard Type Research Articles

Effective single-band Hamiltonian for electron-phonon coupling in cuprate superconductors

We derive an effective single-band Hubbard type Hamiltonian for CuO2 planes. The Hamiltonian includes both electron-electron repulsion and electron-phonon coupling to oxygen vibrational modes. We start with first-principles density functional theory parameters and then map onto a single-band model. Unlike previous mappings to a single-band Hamiltonian, ours explicitly preserves the Fermi surface shape and matrix elements of the many-band Hamiltonian. We consider both in-plane oxygen breathing modes as well as out-of-plane tilting modes. The latter modes have a quadratic electron-phonon coupling, and are also highly anharmonic in La2CuO4 based superconductors. The coupling to breathing modes is too small to account for highTc, while the coupling to quadratic modes is much stronger even though they would be neglected in a standard Migdal-Eliashberg approach to superconductivity.

Flux phase of the half-filled band.

The conjecture is verified that the optimum, energy minimizing magnetic flux for a half-filled band of electrons hopping on a planar, bipartite graph is $\pi$ per square plaquette. We require {\it only} that the graph has periodicity in one direction and the result includes the hexagonal lattice (with flux 0 per hexagon) as a special case. The theorem goes beyond previous conjectures in several ways: (1) It does not assume, a-priori, that all plaquettes have the same flux (as in Hofstadter's model); (2) A Hubbard type on-site interaction of any sign, as well as certain longer range interactions, can be included; (3) The conclusion holds for positive temperature as well as the ground state; (4) The results hold in $D \geq 2$ dimensions if there is periodicity in $D-1$ directions (e.g., the cubic lattice has the lowest energy if there is flux $\pi$ in each square face).

The quasiparticle properties of UPt3 and the high-Tc cuprates

The dynamic fluctuations due to localized Hubbard type of effective interactions, U and J, are calculated perturbatively up to second order around the local density approximation (LDA) electronic structure. We have found for UX3 (X  Ir, Pt, or Au), the mass-enhancement factors are in good agreement with experiment for U = 2eV, and that the trends in the enhancement factors are systematically related to changes in the underlying LDA electronic structure. As for La2CuO4 we find that the dynamic fluctuations are small despite the large effective interaction. Further, our approach reproduces the insulating ground state and the magnetic moment correctly. For the doped case [La2-xBaxCuO4 (x ≠ 0)] we find that even though the mass enhancement is small, there is a significant broadening of the quasiparticles close to the Fermi energy.

Material properties of one-dimensional systems studied by path-integral quantum Monte Carlo simulations and an analytical many-body model

Feynman path-integral quantum Monte Carlo (QMC) simulations and an analytic many-body approach are used to study the ground state properties of one-dimensional (1D) chains in the theoretical framework of model Hamiltonians of the Hubbard type. The QMC algorithm is employed to derive position-space quantities, while band structure properties are evaluated by combining QMC data with expressions derived in momentum (k) space. Bridging link between both representations is the quasi-chemical approximation (QCA). Electronic charge fluctuations and the fluctuations of the magnetic local moments are studied as a function of the on-site density and correlation strength, which is given by the ratio between two-electron interaction and kinetic hopping. Caused by the non-analytic behaviour of the chemical potential μ = ∂E/∂ (with E denoting the electronic energy), strict 1D systems with an on-site density of 1·0 do not exhibit the properties of a conductor for any non-zero ...

Many-body vertex corrections on quasiparticle properties of two-dimensional electron systems.

We calculate theoretically the lifetime, the effective mass, the renormalization factor, and the exchange-correlation-induced band-gap renormalization for quasiparticles in two-dimensional electron systems. In our theory we go beyond the usual random-phase approximation by including many-body vertex corrections of the Hubbard type in the self-energy and the dielectric function of the electron gas. We find that in narrow quantum wells vertex corrections may be quantitatively significant, bringing calculated results close to the experimental data, especially for the case of the band-gap renormalization. In general, vertex correction is found to be more important for narrower quantum wells and for lower electron densities.

The effect of electronic correlations on banding in low dimensional systems

We investigate the influence of many body effects on banding in systems with low dimensionality. This includes organic solids, polymers and layered materials. It is argued in this paper, that many-body effects can become important in generating quasi-3-dimensinality. We suggest that this effect is particularly important in doped systems where there are locally regions of free charge like in doped polymers and in highTc superconductors. Various mechanisms for enhanced many-body induced banding in the weak direction are discussed. This includes polarisation effects and correlations of the Hubbard type.

Stoner exchange interaction in transition metals.

The theory of magnetism in transition metals is often expressed in terms of a Stoner exchange parameter I. Results for I are presented from electronic-structure calculations with correlations for a d-band-only Hubbard type of Hamiltonian. The main effects are: (a) Due to correlation, I depends substantially on the volume via the bandwidth. (b) There are analogous corrections to lattice constants calculated with the local-density approximation (LDA). (c) I also depends on magnetization, band filling, and crystal structure. (d) In Ni the reduction of charge and spin fluctuations almost eliminates the contribution to I of exchange between different orbitals. (e) I computed in the LDA is usually overestimated by 10%--20% because the LDA largely neglects spin correlations.

Momentum density and Fermi surface of YBa2Cu3O7

To understand recent 2D-ACAR experiments, we have carried out a calculation of the momentum density and Fermi surface of a 123 compound. The calculation is based on a tight-binding model, the parameters of which have been obtained from a fit to a self-consistent LMTO band structure. The effect of electron correlations on momentum density is studied using a Hubbard type Hamiltonian. By using an alloy analogy, the Green's function for the model has been obtained within the coherent potential approximation. Results are obtained for various values of the on-site electron-electron interaction and are compared with the experimental results.

Spin susceptibility in a two-dimensional electron gas.

The problem of the many-body enhancement of the static spin susceptibility at long wavelengths and its relation to the quasiparticle effective mass is investigated for a normal electron gas in two-dimensional space as a function of the electronic density. We start from a discussion of the results of the simple Hartree-Fock approximation for various interaction potentials and proceed to develop a complete theory. We find that the effects of the electron-electron interaction are significantly larger than in the familiar three-dimensional case. Our approach is based on a new self-consistent scheme which goes beyond the simple random-phase approximation by explicitly allowing for charge- and spin-fluctuation-induced vertex corrections of the Hubbard type. We show that when the latter are neglected, the many-body enhancement of the spin susceptibility can be cast in a remarkably simple and elegant analytic form.

On the functional integral method applied to models with Hubbard type interaction

To avoid the arbitrariness of the functional integral method, originating from the numerous different ways to rewrite the Hubbard interaction, a self-consistent procedure is given based on a generalized quadratic form in terms of spins and quasispins.

Two-band model with off-diagonal occupation dependent hopping rate: enhancement of the coupling and superconductivity

Two-band hopping model is treated on a two-dimensional square lattice. The atoms are located at the corners and the middles of the edges of the squares. In addition to the strongly overlapping orbitals of the atoms, there are extra orbitals at the corners, which are weakly hybridized. The assumption is made that the Fermi level is inside the broad band and is very near to the narrow band formed by the extra orbitals. The Hamiltonian is Hubbard type, but the off-diagonal part of the two-site interaction t̃ is kept also where one creation or annihilation operator acts on the extra orbital and the others on one of its neighbors. The weak coupling t̃ is enhanced by the on-site Coulomb repulsion at the corners, which enhancement is a power function of the ratio of the broad band width and the narrow band position measured from the Fermi level. That enhancement is obtained by summation of logarithmic Kondo-type corrections of orbital origin, which reflects the formation of a ground state of new type with strong orbital and spin correlations. Interaction between the particles of the broad band is generated by processes with one heavy and one light particle in the intermediate state. That interaction strongly depends on the momenta of the particles. The generated interaction can result in attractive interaction, but particular parity of the different orbitals are required in the given approximation. The model clearly demonstrates that repulsive interaction can result in superconductivity.

Electronic and vibrational absorption spectra of radical cation salts: (DIMET) 2MF 6

The optical properties of the radical cation salts based on the unsymmetrical molecule dimethylethylenedithiotetrathiafulvalene (DIMET) and associated with centrosymmetrical counter ions (AsF 6 − and SbF 6 −) have been explored and compared with other salts. Their vibrational spectra (IR and Raman spectroscopies) as well as the electronic charge transfer bands have been studied between 300 K and 10 K. As in other (2-1) radical cation salts characterized by a structural organization of centrosymmetric dimers, we have found vibronic lines at any temperature, but they behave differently for the two salts. We have also fitted the C.T. absorption bands using a Drude-Lorentz model, which allows us to show that the present energy gaps are basically of a Hubbard type. As confirmed by a comparison with the known magnetic properties, we find that the electronic correlations are the dominant interactions in these compounds with narrow electronic bands.

Optical properties of radical cation salts derived from the TTF molecule: Evidence for electronic correlations and phase transitions in organic conductors

Abstract Following a general presentation of the organic conductors which belong to the series of radical cation salts derived from the tetrathiafulvalene molecule we analyze the characteristic charge transfer absorption bands observed in these mixed valence compounds. Using a Drude-Lorentz model we show that the energy gap present in these materials is basically of the Hubbard type. Nevertheless we observe also in specific cases additional contributions due to either a periodic lattice distortion or a counter-ion electrostatic perturbation. We conclude finally that the electronic correlations are the dominant interactions in these narrow 1d electronic band systems.

The effects of dried poultry dropping (DPD) and dried activated sewage sludge (DASS) on broiler carcass quality

An experiment was conducted with 280 hubbard type broiler chicks, for 9 weeks, to evaluate the effect of dried poultry droppings (DPD) and dried activated sewage sludge (DASS) on broiler carcass quality. There were significant differences (P < 0·05) between treatments for percentage dressed carcass and total edible meat. DPD beyond the 5% level did not improve carcass quality, but birds on 5% DASS and DPD plus DASS mixture diets yielded carcasses of quality comparable with those on the control ration. There were no significant differences in cooked meat texture, tenderness and juiciness between the control and substituted diets, but taste scores for flavour indicated a preference for meat from broilers on the unsubstituted control diet, while meats from 10% DPD and DASS diets were the least palatable.

Alloy Analogy for the Multi‐Band Hubbard Hamiltonian

AbstractA systematic derivation of the alloy analogy for the multi‐band Hamiltonian of the Hubbard type is given. The formalism, of the Hubbard atomic operators is used and the decoupling procedure is applied to the double‐time Green functions. The solution is equivalent to the coherent potential approximation for a set of effective multi‐component alloys and in the single‐band case it is identical to the Hubbard III solution. The theory is valid both, for crystals and for disordered alloys. It is applicable also for the translationally non‐invariant ground state corresponding e.g. to an arbitrary magnetic ordering.

Separable interactions and liquid 3He: IV. Extrema of Landau expansion

In a previous paper we have derived the Landau expansion in terms of the 18 real order parameters for the ordered phases of liquid 3He in the presence of a magnetic field starting from a model hamiltonian which contains an l=1 pairing interaction of the BCS type and a contact term of the Hubbard type. In this paper we present a systematic treatment of the extrema of this Landau expansion under a so-called inertia condition which we believe to cover the physically interesting cases.

Separable interactions and liquid 3He : III. Landau expansion in the presence of a Hubbard interaction

In this paper we derive the Landau expansion for the ordered phases of liquid 3He in the presence of a magnetic field starting from a model hamiltonian which contains an l = 1 pairing interaction of the BCS type and a contact term of the Hubbard type. In the derivation use is made of an exact theorem in the theory of separable interactions and the contribution from the Hubbard interaction is evaluated in second order perturbation calculation. Some typical differences with the results based on a spin fluctuation theory are mentioned.

The spin fluctuation of an impurity in the transition metal alloys

We make the functional integral formalism of the Hubbard type applicable to the localized large-fluctuation of spin in the transition metal alloys over a wide temperature range with practical models. It is found that the calculated magnetic susceptibilities, when applied to the symmetric Anderson model for T = 0, are in numerical agreement with those given by the exact solution.

Electronegativity and a model hamiltonian for chemical applications

A study is made of the connection between a one-electron model hamiltonian of the Anderson—Hubbard type and the electronegativity, both for free atoms and for simple binary compounds. Non-linear terms in the valence electron occupation number must be included in the hamiltonian in addition to the usual linear tenn. It is found that interatomic interactions occurring in the compound increase the non-linearity substantially over that for the separated atomic constituents. This approach improves the physical understanding of the connection between the clectronegativities of the cation and the anion and (1) the Fermi energies (work functions) of solid compounds and (2) charge transfer in heteronuclear molecules. Charge transfer is specifically discussed for donor-acceptor organic solids and for strongly polar molecules with mutual cation-anion polarization effects included.

A note on magnon life-time in itinerant electron ferromagnetic alloys

A model of a binary ferromagnetic alloy A 1− c B c is discussed in terms of a single band Hubbard type hamiltonian. It is shown by summing up contribution of single-site scattering to all orders, that the inverse life time of long-wavelength magnons due to disorder scattering is proportional to q 5 and, in the limit c ⪡ 1, to the concentration c .