A model to describe electronic correlations in energy bands is considered. The model is a generalization of the conventional Hubbard model that allows for the fact that the wave function for two electrons occupying the same Wannier orbital is different from the product of single-electron wave functions. We diagonalize the Hamiltonian exactly on a four-site cluster and study its properties as a function of band filling. The quasiparticle weight is found to decrease and the quasiparticle effective mass to increase as the electronic band filling increases, and spectral weight in one- and two-particle spectral functions is transferred from low to high frequencies as the band filling increases. Quasiparticles at the Fermi energy are found to be more ``dressed'' when the Fermi level is in the upper half of the band (hole carriers) than when it is in the lower half of the band (electron carriers). The effective interaction between carriers is found to be strongly dependent on band filling becoming less repulsive as the band filling increases and attractive near the top of the band in certain parameter ranges. The effective interaction is most attractive when the single-hole carriers are most heavily dressed, and in the parameter regime where the effective interaction is attractive, hole carriers are found to ``undress,'' hence become more like electrons, when they pair. It is proposed that these are generic properties of electronic energy bands in solids that reflect a fundamental electron-hole asymmetry of condensed matter. The relation of these results to the understanding of superconductivity in solids is discussed.
The spectral functions of one hole in the t-J and one-band Hubbard models are calculated using exact diagonalization techniques on small lattices. Results for the t-
Jz model are also presented. For the t-J model we found that there is a quasiparticle at the bottom of the hole spectrum with an energy well approximated by
Eh=-3.17+2.83
J0.73 (for 0.1\ensuremath{\le}J\ensuremath{\le}1.0, t=1) on a 4\ifmmode\times\else\texttimes\fi{}4 lattice. The rest of the spectrum is not incoherent: We identified at least two other peaks following a similar power-law behavior with J. We speculate that the J dependence of the results can be explained by a model where the hole is trapped in a confining potential as in the Ising limit. The bandwidth of the hole is linear in J in the region 0.1\ensuremath{\le}J\ensuremath{\le}0.4 although a power-law behavior is not excluded. The spectral weight of the quasiparticle grows like
J0.5 in the same region. We present new analytical results in the large J/t limit to understand the motion of the hole: In perturbation theory it can be shown that the momentum of the hole at large J/t is k=(\ensuremath{\pi},\ensuremath{\pi}) changing to k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2) at intermediate J/t in agreement with numerical and spin-waves results. We show analytically and numerically that the bandwidth of the quasiparticle is of order t in the large J/t limit. This result corresponds to a spin-liquid state. The one-hole spectral function of the Hubbard model is obtained for lattices with 8 and 10 sites. A quasiparticle is also observed in this case. The bandwidth and the relation with the t-J model are discussed and a comparison with recent Monte Carlo results is made. We also review and extend previous results for the ground-state properties of the t-J model.
We study the t-J and the Hubbard models at zero temperature using exact-diagonalization techniques on \ensuremath{\surd}10 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}10 and 4\ifmmode\times\else\texttimes\fi{}4 sites clusters. Quantum Monte Carlo simulation results on larger lattices are also presented. All electronic fillings have been analyzed for the three models. We have measured equal-time correlation functions corresponding to various types of order (ranging from ``standard'' staggered spin order to more ``exotic'' possibilities like chiral order), as well as various dynamical properties of these models. Upper bounds for the critical hole doping (
xc), where long-range antiferromagnetic order disappears, are presented. It was found that
xc is very small in agreement with experiments for the high-
Tc superconductors. For example, in the t-J model, ${\mathit{x}}_{\mathit{c}}$0.08 at J/t=0.4. However, short-distance spin correlations are important up to much higher dopings producing a sharp well-defined spin-wave-like peak in S(q=(\ensuremath{\pi},\ensuremath{\pi}),\ensuremath{\omega}). Regarding the possibility of phase separation in the Hubbard model, we have studied the behavior of the density of particles, 〈n〉, as a function of the chemical potential, using the Lanczos method on a 4\ifmmode\times\else\texttimes\fi{}4 Hubbard cluster, finding no indications of phase separation for any value of U/t. Then, we conclude that the t-J model at small J/t should not phase separate.In order to compare theoretical predictions with photoemission experiments, we evaluated the electronic density of states N(\ensuremath{\omega}), of the Hubbard and t-J models at several doping fractions. We found that upon doping the antiferromagnetic gap is filled for U\ensuremath{\sim}8t or smaller. The chemical potential moves across the insulating gap as one goes from electron to hole doping of the half-filled cluster, in agreement with x-ray absorption experiments but at variance with photoemission experiments. We have also calculated the optical conductivity, ${\mathrm{\ensuremath{\sigma}}}_{1}$(\ensuremath{\omega}), of the Hubbard and t-J models at all dopings on 4\ifmmode\times\else\texttimes\fi{}4 clusters. Results are compared with experiments and the weight of the Drude peak is presented as a function of couplings and dopings. Spectral weight found at small frequencies is associated with the mid-infrared band observed experimentally in ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$
SrxCuO4, and with the states filling the insulating gap in photoemission experiments. An overall good agreement with experiments in the normal state was found. Regarding the possibility of superconductivity n these models, we have studied s-, d-, and p-wave pairing correlations. Naively, the d-wave channel seems enhanced near half filling while the extended s-wave channel seems enhanced from half filling up to 40% doping.However, we found that the enhancement comes from short-distance effects and, thus, no numerical indications of superconductivity were found in these models. We emphasize the importance of analyzing the pairing correlations as a function of distance to distinguish between short- and long-distance effects in the susceptibilities. We also observed that spiral order is enhanced at small J/t and low doping. Uniform chiral rder is suppressed by dynamical holes while staggered chiral order may be enhanced, although with a small plaquette order parameter. We conclude with the observation that the simple one-band Hubbard model with intermediate values of U\ensuremath{\sim}8t may account for many of the ``anomalous'' properties of the normal state of the high-
Tc superconductors.
The one-dimensional Hubbard model is characterized by charge-spin separation, but nevertheless in the doped system \ensuremath{\sigma}(\ensuremath{\omega}>0) does not vanish due to a small remaining coupling between charge and spin degrees of freedom. We derive an effective Hamiltonian and give in leading order (\ensuremath{\sim}
J2) an analytic expression for \ensuremath{\sigma}(\ensuremath{\omega}) for the case of the Mott insulator doped with one hole. The complete frequency dependence in the strong-coupling limit of the Hubbard model and for the t-J model agrees with results from exact diagonalization. The limit \ensuremath{\sigma}(\ensuremath{\omega}\ensuremath{\rightarrow}0) at T=0 is found to be very different for the two models, i.e., \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{3/2}$ in the strong-coupling limit and \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}1/2}$ for the t-J model.
The author calculates an exact expression for the Green function of a single hole in a Neel background, for finite Ising interaction J z identical to 4t 2 /U where t is the hopping (overlap) integral in the Hubbard model and U the usual on-site interaction. In 1D for fixed boundary conditions, loops are absent and thus the expression is exact and independent of the retraceable path approximation, while in 2D the expression is exact to within the exclusion of loops. The spectral function A( omega ) shows delta-function peaks at well defined energy spacings, with damping only at frequencies omega >5/2J z different from earlier results. These peaks are necessary for the existence of quasiparticles. The author presents an argument that, for sufficiently large U, the discrete spectrum in A( omega ) merges to a continuous 'band' as the weight varies as J z of the poles vanishes in the U= infinity limit and hence that use of the latter does not necessarily imply incoherent behaviour in the system.
We present analytic expressions for the exact density functional and Kohn-Sham Hamiltonian of simple tight-binding models of correlated electrons. These are the single- and double-site versions of the Anderson, Hubbard, and spinless fermion models. The exact exchange and correlation potentials keep the full nonlocal dependence on electron occupations. The analytic expressions allow us to compare the Kohn-Sham eigenstates of exact density functional theory with the many-body quasiparticle states of these correlated-electron systems. The exact Kohn-Sham spectrum describes correctly many of the nontrivial features of the many-body quasiparticle spectrum such as, for example, the precursors of the Kondo peak. However, we find that some pieces of the quasiparticle spectrum are missing because the many-body phase space for electron and hole excitations is richer.