Optical Conductivity in the Hubbard Model

Abstract

Frequency dependent conductivity σ(ω) is calculated for the asymmetric Hubbard model in the limit of strong correlations, U ≫| t αβ |, where t αβ are the hopping integrals for the lower (α= β=1) or the upper (α= β=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 σ(ω) is obtained with essentially two contributions in the low frequency region (Drude part) and in the high frequency region, \(\hbar\omega \simeq U\). It is shown that the Drude relaxation rate is proportional to [( t αα ) 2 - ( t 12 ) 2 ] 2 and goes to zero for the symmetric Hubbard model ( t αβ = t ) where σ(ω) ∝δ(ω). It is suggested that for electronically doped copper oxides spin fluctuation relaxation rates should be much weaker then for hole doped ones.