Optical conductivity in the Hubbard model

Frequency dependent conductivity sigma(omega) is calculated for the asymmetric Hubbard model in the limit of strong correlations, U much greater than \t(alpha beta)\, where t(alpha beta) are the hopping integrals for the lower (alpha = beta = 1) or the upper (alpha = beta = 2) Hubbard bands. By applying the memory function technique in terms of the Hubbard operators relaxation rates due to electron scattering on spin and charge dynamical fluctuations are calculated. A generalized Drude law for sigma(omega) is obtained with essentially two contributions in the low frequency region (Drude part) and in the high frequency region, <(h)over bar omega> similar or equal to U. It is shown that the Drude relaxation rate is proportional to [(t(alpha alpha))(2)-(t(12))(2)](2) and goes to zero for the symmetric Hubbard model (t(alpha beta) = t) where sigma(omega) proportional to delta(omega). It is suggested that for electronically doped copper oxides spin fluctuation relaxation rates should be much weaker then for hole doped ones.