Strong-coupling thermodynamics of the Hubbard model

Thermodynamic properties of the half-filled-band Hubbard model are calculated in the strong-coupling regime for a simple cubic structure, using the Bogoliubov variational principle. When the Coulomb-interactionV _o exceeds the bandwidthJ, we find a phase transition from a condensed phase of itinerant electrons into a state of localized ones at a transition temperature which exhibits the asymptotic behaviourT ₀J ²/V ₀ at largeV ₀.     

Strong-coupling thermodynamics of the Hubbard model

Thermodynamic properties of the half-filled-band Hubbard model are calculated in the strong-coupling regime for a simple cubic structure, using the Bogoliubov variational principle. When the Coulomb-interactionV _o exceeds the bandwidthJ, we find a phase transition from a condensed phase of itinerant electrons into a state of localized ones at a transition temperature which exhibits the asymptotic behaviourT ₀J ²/V ₀ at largeV ₀.     

Strong-coupling perturbation theory of the Hubbard model

The strong-coupling perturbation theory of the Hubbard model is presented and carried out to order (t/U)⁵ for the one-particle Green function in arbitrary dimension. The spectral weight is expressed as a Jacobi continued fraction and compared with new Monte-Carlo data of the one-dimensional, half-filled Hubbard model. Different regimes (insulator, conductor and short-range antiferromagnet) are identified in the temperature-hopping integral (T,t) plane. This work completes a first paper on the subject (Phys. Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules and higher-order results. In addition, the non half-filled case, infinite resummations of diagrams and the double occupancy are discussed. Various tests of the method are also presented. Received 25 October 1999     

Thermodynamics of the neutral Hubbard model

By use of Bogoljubov's variational principle the free energy of the neutral Hubbard model is calculated as a function of the total spinS _z . A transition from an antiferro-magnetic to a paramagnetic phase is found for all values of the coupling constantV ₀. The calculations are performed for the simple cubic and the body-centred cubic lattice; some numerical results are given for the transition temperature, the free energy, the sublattice magnetization, the transversal magnetic susceptibility and the response to a finite magnetic field.     

The orbital susceptibility of the neutral Hubbard model

Using the test Hamiltonian introduced by Dichtel, Jelitto, and Koppe we calculated the linear response of the model to a small magnetic field, and determined therefrom the static susceptibility for the case of an s. c. lattice. Numerical results were obtained for this type of lattice. The susceptibility is found to be rather independent of temperature in a wide range of absolute temperature. The ratio of the diamagnetic to the paramagnetic susceptibility (which was calculated in a previous paper) goes to zero in the limit of zero hopping.     

The ground state of the neutral Hubbard model

The ground state energy of the neutral Hubbard model is calculated by BCS methods for all values of total spinS _z . Numerical results are given for the simple cubic and for the body centred cubic lattice. Antiferromagnetic ordering and a finite paramagnetic susceptibility is found for all values of the coupling constantV ₀.     

Electrical and thermal conductivity of the neutral Hubbard model

The electrical and thermal conductivities are calculated in the weak coupling region within the half-filled-band Hubbard model. A derivation of the energy-current operator is given and the electron-phonon interaction is introduced into the model. Using a variational principle for the Boltzmann equation the average relaxation times are determined for both transport mechanisms. The results are compared with the resistance due to impurity scattering. For numerical purposes a combined density of states is established.     

Thermodynamic properties of the one-dimensional Hubbard model

We discuss the thermodynamic behaviour of the one-dimensional Hubbard model in the narrow-band regime, where the intra-atomic Coulomb-repulsion is large compared to the bandwidth. An approximation scheme on a perturbative basis is developed which applies for all temperatures. First order perturbation theory is performed for arbitrary electron densities; second order perturbation theory is discussed in the case of the half-filled band. Also the one-particle Green's function is calculated. Our approximation agrees excellently with numerical calculations. By comparison with exact results, which are available for some special limits, the range of validity of our approximation is estimated.     

Superconducting properties of the attractive Hubbard model

A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently used to study the effect of electron correlations on normal-state properties. An approximation to the set of equations is solved numerically in the intermediate coupling regime, and the one-particle spectral functions are found to have four peaks. This feature is traced back to a peak in the self-energy, which is related to the formation of real-space bound states. For comparison we extend the moment approach to the superconducting state and discuss the crossover from the weak (BCS) to the intermediate coupling regime from the perspective of single-particle spectral densities.     

Spectral properties of the attractive Hubbard model

We calculate the spectral functions, the band structure and the density of states of the 2D attractive Hubbard model in the intermediate coupling regime (i.e. the crossover regime between BCS theory and Bose-Einstein Condensation) using a grand canonical quantum Monte-Carlo approach and a maximum entropy procedure. The evolution of the spectral properties as a function of temperature is discussed. In particular, on lowering the temperature, we find a splitting of the single band present at high temperatures into several distinct branches, the number of which depends on the temperature. Received: 7 July 1998 / Accepted: 30 July 1998     

Strong-coupling method in the kronig-penny model

The strong-coupling approximation is investigated in a model one-dimensional potential. It is shown that even for large values of the overlap integrals S = 0.5 the approximation gives good results when a sufficiently large number of neighbors is taken into account. Otherwise, the approximation can give spurious extrema in the density of states. A modified strong-coupling method is formulated having considerable advantage over the usual method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 27–30, March, 1975.     

Critical properties of the half-filled Hubbard model in three dimensions

By means of the dynamical vertex approximation (DΓA) we include spatial correlations on all length scales beyond the dynamical mean-field theory (DMFT) for the half-filled Hubbard model in three dimensions. The most relevant changes due to nonlocal fluctuations are (i) a deviation from the mean-field critical behavior with the same critical exponents as for the three dimensional Heisenberg (anti)ferromagnet and (ii) a sizable reduction of the Néel temperature (T(N)) by ~30% for the onset of antiferromagnetic order. Finally, we give a quantitative estimate of the deviation of the spectra between DΓA and DMFT in different regions of the phase diagram.