We consider a Hubbard model in which electrons are locally coupled to the lattice and form polarons. The frequency-dependent polaron conductivity ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{pot}}$(\ensuremath{\omega}) is calculated in the narrow-band limit as a function of electron density. There are two contributions: a band term that arises from coherent motion of dressed electrons and a hopping term that describes the incoherent process by which electrons ``shake off'' their polaron distortion. The possible relevance of these results to the structure in \ensuremath{\sigma}(\ensuremath{\omega}) observed in high-
Tc superconductors is briefly discussed.
Recent numerical results for the single-particle spectral function and optical conductivity of the two-dimensional Hubbard and t−J models are reviewed. Already for two holes in systems of sixteen to twenty sites (≥ 10% doping) a large electronic Fermi surface, compatible with Luttinger’s theorem, is observed. The full single-particle Green’s function is examined, and is shown to exhibit quasiparticle-like behavior, with dispersion consistent with the band structure of the non-interacting limit, and band width scaling approximately as J for J smaller than t. The optical conductivity of the Hubbard and t−J models is shown to have many features in common with recent experiments on copper oxide superconductors. The importance of the often neglected 3-site terms which arise in the derivation of the t−J model from the Hubbard model for optical properties is discussed.
In this paper, the low-temperature (${k}_{B}T\ensuremath{\ll}U$) frequency-dependent $\ensuremath{\sigma}(\ensuremath{\omega})$ conductivity in a half-filled Hubbard chain is calculated to the lowest order in the parameter
Ut and in closed form to all orders in $\frac{t}{\ensuremath{\omega}}\ensuremath{-}U$. Here
t is the nearest-neighbor hopping integral and
U the intra-atomic Coulomb interaction. The problem is formulated in terms of the number of random walks of an electron and a hole which leave the spin configuration unchanged, at temperatures such that ${k}_{B}T\ensuremath{\ll}t\ensuremath{\ll}U$ (where
kB is Boltzmann's constant). The conductivity then depends on spin configuration, and for both the antiferromagnetic (AF) (
T=0 K) ground state and the equiprobable or random arrangement (
R) (${k}_{B}T\ensuremath{\gg}\frac{{t}^{2}}{U}$) an exact expression is found. For the partially disordered regime ($T\ensuremath{\simeq}{T}_{N}$) the thermodynamical averaging is expressed in terms of a phenomenological spin-spin correlation length
l which interpolates between the AF and
R exact limits. This solution is such that for $l=\ensuremath{\infty}$ the AF line shape is recovered except at the center of the spectrum (i.e., at $\ensuremath{\omega}=U$), where the absorption always diverges logarithmically. For a ferromagnetic (
l=0) arrangement induced by a magnetic field, the absorption then vanishes. The line shapes obtained have sharp edges at $|\ensuremath{\omega}|=U\ifmmode\pm\else\textpm\fi{}4t$ for all temperatures. At the critical value of
4t=U the AF ground state is found to undergo a metallic transition. A closed-form analytical expression in terms of the three elliptical integrals is given for the absorption lines. Except for the AF case, which has a square-root edge singularity, the absorption is found to vanish linearly. Finally, a comparison is made with some recent calculations.
We study the frequency-dependent electrical conductivity of a structurally disordered single-band Hubbard model near half-filling and in the strong-correlation limit. The electronic transfer integral is assumed to have a quasi-exponential form as used in the impurity-band problem of doped semiconductors. The short-time expansion of the current correlation function is calculated diagrammatically to the second order in the inverse temperature β and up to the seventh order in electronic hopping. Based on this expansion an approximate current correlation function is constructed. By means of the Kubo formula, the configurational average of the electrical conductivity is then calculated to order β2 for various atomic densities. The validity of the high-temperature expansion is examined. We also study the effect of spin polarization on the absorption line shape and the dc resistivity at different temperatures.
We calculate the properties of the two-band Hubbard model using the dynamical cluster approximation. The phase diagram resembles the generic phase diagram of the cuprates, showing a strong asymmetry with respect to electron- and hole-doped regimes, in agreement with experiment. Asymmetric features are also seen in one-particle spectral functions and in the charge, spin, and
d-wave pairing-susceptibility functions. We address the possible reduction of the two-band model to a low-energy single-band one, as it was suggested by Zhang and Rice. Comparing the two-band Hubbard model properties with the single-band Hubbard model ones, we have found similar low-energy physics provided that the next-nearest-neighbor hopping term ${t}^{\ensuremath{'}}$ has a significant value $({t}^{\ensuremath{'}}∕t\ensuremath{\approx}0.3)$. The parameter ${t}^{\ensuremath{'}}$ is the main culprit for the electron-hole asymmetry. However, a significant value of ${t}^{\ensuremath{'}}$ cannot be provided in a strict Zhang and Rice [Phys. Rev. B 37, R3759 (1988); 41, 7243 (1990)] picture where the extra holes added into the system bind to the existing Cu holes forming local singlets. We note that by considering approximate singlet states, such as plaquette states, reasonable values of ${t}^{\ensuremath{'}}$, which capture qualitatively the physics of the two-band model, can be obtained. We conclude that a single-band $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U$ Hubbard model captures the basic physics of the cuprates concerning superconductivity, antiferromagnetism, pseudogap, and electron-hole asymmetry, but is not suitable for a quantitative analysis or to describe physical properties involving energy scales larger than about 0.5 eV.
In this work we obtain the magnetic and thermodynamic properties of the classical Hubbard model. This one is easier to handle than the original Hubbard model, and it maintains fundamental aspects like charge and particle-hole symmetry. We find the relationship between this and the Ising model. For square and simple cubic lattices, the thermodynamic properties and phase diagrams were calculated by Monte Carlo method. We show the behavior of internal energy, specific heat, and magnetic susceptibility as a function of the temperature. For the considered lattices, the ground state is anti-ferromagnetic. The Néel temperatures were found as a function of the electronic interaction in the case of half-filled band. In the limit of vanishing of diverging interaction, our results agree with the Ising model.