On the frequency‐dependent conductivity and the current operator of the Hubbard model

Peter Horsch, W. Stephan

M. Grandadam, J. P. F. LeBlanc

We study the frequency and temperature dependence of the optical conductivity in the weakly coupled two-dimensional Hubbard model using a renormalized perturbative expansion. The perturbative expansion is based on the skeleton series for the current-current correlation function with a dressed Green`s function and the results are obtained directly on the real frequency axis using Algorithmic Matsubara Integration (AMI). The resulting conductivity shows a temperature-independent power law behaviour in the intermediate frequency regime. Moreover, the associated transport scattering time and renormalized mass exhibit a Planckian behaviour. We show that the self-energy of the Hubbard model, however, is distinct from existing Planckian models. The Planckian behaviour of the conductivity, observed in optimally doped cuprates for example, can thus be obtained from a different form of self-energy than the Planckian model, such as the weakly coupled Hubbard model at half-filling.

F. Mancini, D. Villani

David L. Huber

L. Tan, J. Callaway

The frequency-dependent (optical) conductivity of the Hubbard model on a three-dimensional cubic lattice is studied through calculations on a small cluster. The interaction strength is varied between the weak- and strong-coupling limits. Results are reported for the half-filled band, and for small hole dopings away from half filling. The formation of a Hubbard gap is observed. Results are related to aspects of the current discussion of the metal-insulator transition in bulk systems.

K. L. Liu

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.