High-frequency optical conductivity of the half-filled Hubbard model, in the strong coupling limit

Abstract

The temperature dependence of the high-frequency optical conductivity of the half-filled Hubbard model is calculated in the strong coupling limit, using the non-crossing approximation. For large dimensionality, d, the electronic spectral density is of the order of the coulomb interaction U in the strong coupling limit, as expected from the arguments of Mott and Hubbard. The value of the gap is renormalized by spin fluctuations and is strongly affected by the dimensionality, in accordance with the Mermin–Wagner theorem. The spin fluctuation energies are governed by Anderson's kinetic exchange, J= t 2/ U, as is the temperature dependence of the gap. The width of the incoherent peaks is due to spin-wave shake off processes and is of the order of U. The intensity of the coherent quasi-particle peaks in the spectral density is renormalized down to small values. The optical conductivity is calculated for various dimensionalities and the results are compared with the exact solutions found in the limits of d→∞ and d=1.