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Physical Review B

Exact diagonalization study of optical conductivity in the two-dimensional Hubbard model

禎通 前川

Published Jan 1, 2005• 0 citations
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Optical and DC conductivity in the two-dimensional t−t′−t′′t-t'-t''t−t′−t′′ Hubbard model near the antiferromagnetic quantum critical point
The optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in the two-dimensional Hubbard model is examined by applying the exact diagonalization technique to small square clusters with periodic boundary conditions up to $\sqrt{20}\ifmmode\times\else\texttimes\fi{}\sqrt{20}$ sites. Spectral-weight distributions at half-filling and their doping dependence in the 20-site cluster are found to be similar to those in a $\sqrt{18}\ifmmode\times\else\texttimes\fi{}\sqrt{18}$ cluster, but different from $4\ifmmode\times\else\texttimes\fi{}4$ results. The results for the 20-site cluster enable us to perform a systematic study of the doping dependence of the spectral-weight transfer from the region of the Mott-gap excitation to lower-energy regions. We discuss the dependence of the Drude weight and the effective carrier number on the electron density at a large on-site Coulomb interaction.
We calculate the total and low-frequency spectral weight of the optical conductivity of the two-dimensional Hubbard model for various values of the interaction strength and carrier concentration. In some limits we obtain exact results and bounds. For general parameter values we obtain estimates using the variational Monte Carlo technique. We show that our results disagree with those obtained by exact diagonalization of small systems, and argue that the latter are less accurate because of finite-size effects.