The conductivity for half-filled disordered Hubbard model in different interaction regimes is studied using a typical medium dynamical mean-field theory. The Kubo formula with the geometrically averaged Green function is used to calculate the optical and dc conductivity of the system. The dependence of the conductivities in the model on the random potential and temperature in the weak and intermediate interaction regimes is investigated numerically. It is shown that in the weak interaction regime at a fixed temperature the optical conductivity at low frequencies as well as the dc conductivity get decreased as disorder strength increases. Whereas in the intermediate interaction regime, the results show a reentrant effect of the insulating phases. Our dc conductivity of a non-interacting disordered system is consistent with those known in the literature and our other results are in agreement with the phase diagram obtained by using typical medium theory with different impurity solvers.
Abstract The chemical potential μ and the electrical dc conductivity σ in the one‐dimensional Hubbard model in the strong‐coupling region U≫t (U intra‐atomic Coulomb energy, –t nearest‐neighbour hopping integral) are calculated as functions of temperature and electron density n. In the non‐half‐filled band case n ≠ 1 the Bari‐Kaplan approximation lim (σ/t2) is shown to yield an un magnified image physical singularity in the dc conductivity at T = 0 which is connected with the discontinuity of the zero‐temperature chemical potential at n = 1. An improved calculation for n ≠ 1 going beyond the Bari‐Kaplan approximation (i.e. taking into account the band terms in μ and σ/t2) yields a finite zero‐temperature conductivity which is proportional to the first power in t. For small deviations from the half‐filled band case the conductivity as a function of increasing temperature subsequently shows a metal‐like behaviour, a semiconductor‐like behaviour, and a repeated decrease at high temperatures.
We study the temperature-dependent spin susceptibility of a structurally disordered Hubbard model with a quasi-exponential transfer integral based on a hydrogenic 1 s wavefunction. The electronic hopping is treated perturbatively up to fourth order. The susceptibility is calculated for various atomic concentrations and electronic densities and for different strengths of on-site Coulomb repulsion. Contact is made with the measured susceptibility of lightly doped semiconductors. The possibility for ferromagnetism in the model is examined and conclusions analogous to Nagaoka's theorem and Kanamori's theory are obtained. Finally, using a generalized Kirkwood superposition approximation for the many-body distribution functions, we have investigated the influence of short-range atomic correlation on the magnetic properties.
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 density of states for a structurally random Hubbard model with a half-filled band. Calculations are carried out with the hopping integral t(R) obtained from a hydrogenic 1S wave function and with an on-site Coulomb repulsion [Formula: see text]. The equation of motion for the retarded single-particle Green's function is treated in the Hubbard III decoupling approximation. The configurational averaging for the Green's function is simplified using the approximation of Kikuchi. Coefficients in the locator–interactor expansion are calculated analytically up to seventh order in t. Several approximants for this formal series are investigated, including Padé approximant, continued fraction approximation, and quadratic Padé approximant. The last two approximants yield densities of state in satisfactory agreement with the result of Aoki and Kamimura in the high concentration region and our results are expected to represent an improvement for intermediate densities. However, for very low densities the Hubbard III scheme will underestimate the effect of spin correlations and our previous treatment in the U = ∞ limit would be more appropriate for the lower Hubbard band.