On the solutions of the infinite U Hubbard model through orthofermions

We reinforce our earlier arguments for the soundness of the orthofermion approach to the infinite U Hubbard model by studying the distribution and the partition functions for a system of noninteracting orthofermions as well as for two systems of noninteracting orthofermions coupled through inter system single particle hopping.     

On ferromagnetism in the Hubbard model

We use a simple variational procedure for strictly excluding a totally ferromagnetic groundstate of the Hubbard model for the cubic lattices and a certain range of values of the electron concentrationn _e and the Coulomb repulsionV _o. The curve bounding this domain becomes exact in the limit ofn _e → 1, previously considered by Nagaoka, and leads to qualitatively correct results also in the opposite limiting cases ofn _e → 0, and 2, which were investigated by Kanamori.     

On high-temperature expansions of the Hubbard model

We discuss the application of the high-temperature expansion method to the Hubbard model. We recalculate the expansion series of the susceptibility up to the sixth order in the transfer matrix element,t, in the strong correlation limit, and up to the fourth order int in case that the repulsive potential,U, is finite, butt/U 1. It is seen that the convergence of the series is very poor.     

On the onset of antiferromagnetism in the Hubbard model

It is proved that there is no antiferromagnetic solution to the Hubbard model for a half-filled band, within the alloy analogy and the coherent potential approximation.     

On the ground state of the half-filled Hubbard model

We calculate the ground state of the half-filled Hubbard model and its energy by starting from a spindensity wave approximation and improving it by incorporating transverse spin fluctuations. The calculations are done by employing a projection method. The quality of the proposed approximation is particularly high for intermediate and large Coulomb repulsionU, where it exceeds considerably e.g. that of the Gutzwiller projected spin-density wave state. To ordert ²/U (wheret is the hopping matrix element), our approximation is shown to be equivalent to a recent Coupled Cluster calculation for the Heisenberg antiferromagnet. Finally we show how to ordert ²/U the linear spin-wave approximation for the Heisenberg antiferromagnet may be obtained.     

Disorder effects in the BCS-BEC crossover region of the attractive Hubbard model

We study the disorder effects upon superconducting transition temperature T _c and the number of local pairs within the attractive Hubbard model in the combined Nozieres-Schmitt-Rink and DMFT + Σ approximations. We analyze the wide range of attractive interaction U, from the weak coupling region, where instability of the normal phase and superconductivity are well described by the BCS model, to the limit of strong coupling, where superconducting transition is determined by Bose-Einstein condensation of compact Cooper pairs, forming at temperatures much higher than superconducting transition temperature. It is shown that disorder can either suppress T _c in the weak coupling limit, or significantly enhance T _c in the case of strong coupling. However, in all cases we actually prove the validity of generalized Anderson theorem, so that all changes in T _c are related to change in the effective bandwidth due to disorder. Similarly, disorder effects on the number of local pairs are only due to these band-broadening effects.     

On the one-dimensional Hubbard model away from half-filling

We study the spectrum of the one-dimensional Hubbard model near the half-filled band, i.e. for electronic densityn=1–, 1, and also in the low-density limit,n1. Ground state and excited states are described, by integral equations which are derived from the Bethe Ansatz. These equations, which can be solved analytically only in the case of half-filling (=0), are investigated systematically in both limits 1,n1. Appropriate expansions of the momenta and energies of the ground state and the excited states as well as correlation exponents are determined.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-JülichSimilar equations have been derived by Matveenko [3] using a different method     

On superconducting pairing in the two-band Hubbard model

A two-band Hubbard model for highly hybridized copper 3d(x ²–y ²) and oxygen 2p(x,y) electrons in CuO₂ plane with strong Coulomb repulsion at copper sites is considered. A real-space pairing mechanism induced by antiferromagnetic interaction of Kondo type is treated. To avoid the Gutzwiller approximation the projection technique for two-time Green functions for Hubbard operators is employed. It is shown that due to rigorous restriction of no double occupancy at copper sites the exchange-mediatedp-d pairing with a site-independent gap function isabsent.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

On the integrability of the SU(N) Hubbard model

We exhibit explicitly the intertwiner operator for the monodromy matrices of the SU(N) Hubbard model recently proposed by Maassarani [Phys. Lett. A 239 (1998) 187]. This produces a new family of non-additive R-matrices and generalizes an earlier result by Shastry [Phys. Rev. Lett. 56 (1986) 2453; J. Stat. Phys. 30 (1988) 57].     

Simulations of the Hubbard model

We discuss results of simulations of the Hubbard model of interacting electrons on a lattice. We start with a brief discussion of methodology and point out some of the outstanding problems. We then discuss results of simulations of the model in three, two, and one dimension, particularly in connection with its magnetic and superconducting properties. We conclude with a brief discussion of future directions.     

On the symmetries of the Hubbard model: application to finite-size clusters

We evaluate the density of states of the Hubbard model at half filling on a four-site cluster with periodic boundary conditions. The results are obtained from an exact diagonalization study of the model, where theSU(2) symmetry, the Yang\(\widetilde{SU}(2)\) pseudospin symmetry and the translational invariance of the Hamiltonian are explicitly taken into account.     

On the scaling limit of the 1D Hubbard model at half-filling

The dispersion relations and S-matrix of the one-dimensional Hubbard model at half-filling are onsidered in a certain scaling limit. (In the process we derive a useful small-coupling expansion of the exact lattice dispersion relations.) The resulting scattering theory is consistently identified as that of the SU(2) chiral-invariant Thirring (or Gross-Neveu) field theory, containing both massive and massless sectors.     

Antiferromagnetism in the Hubbard model

The energy spectrum of the two-sublattice Hubbard model is obtained in the static-fluctuation approximation. It is shown how the structure of the energy spectrum is modified as the parameters of the Hubbard model are varied. The ground state of the simple Hubbard model of dimension d=2 is the dielectric antiferromagnetic state. The author derives a consistency equation for the magnetization, which has an antiferromagnetic solution. Fiz. Tverd. Tela (St. Petersburg) 39, 1594–1599 (September 1997)     

The symmetry of the Hubbard model

The spectrum of the Hubbard model shows permanent degeneracy of levels with different symmetries, if one considers only symmetry operators independent of the coupling constant. This suggests the existence of symmetry operators which depend on the coupling constant. We find these highly nontrivial operators and show that they explain the degeneracies in the energy spectrum.Part of project No. P5588 of the Fonds zur Förderung der wissenschaftlichen Forschung in Österreich.     

Ferromagnetism in the Hubbard model

Whether spin-independent Coulomb interaction can be the origin of a realistic ferromagnetism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard models on decorated lattices, which have a special property that the corresponding single-electron Schrödinger equation hasN _d-fold degenerate ground states. The degeneracyN _d is proportional to the total number of sites ||. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close to=N _d/(2||), and paramagnetism when the filling factor is sufficiently small. An important feature of the present work is that it provides examples of three dimensional itinerant electron systems which are proved to exhibit ferromagnetism in a finite range of the electron filling factor.     

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.     

On the CPA treatment of Magnetic Disordered Hubbard model (II)

In this contribution we continue the treatment of the model based on the Hubbard hamiltonian in which the stochastic fields acting at the sites of the atoms can assume arbitrary directions and values due to accepted distribution. The averaging procedure introduced by Brandt and Gross to study the behaviour of the magnetically disordered system is used for a model with stochastically localized magnetic fields, resulting from magnetic moments, at the atomic sites, as previously in I. The coherent potential approximation-like method is employed. The selfconsistency problem is regarded as well as the thermodynamic consequences like density of states, localization function, magnetization, high temperature susceptibility and dc conductivity as functions of temperature are discussed.Supported in part by Polish Academy of Science, Problem MR I. 9. Partly done at Institute of Physics and Chemistry of Metals, Silesian University, Katowice, Poland     

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.