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

The temperature dependence of the high-frequency optical conductivity of th e half-filled Hubbard model is calculated in the strong coupling limit, usi ng the non-crossing approximation. For large dimensionality, d, the electro nic spectral density is of the order of the coulomb interaction U in the st rong coupling limit, as expected from the arguments of Mott and Hubbard. Th e Value of the gap is renormalized by spin fluctuations and is strongly aff ected 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 i ncoherent 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 d ensity is renormalized down to small values. The optical conductivity is ca lculated for various dimensionalities and the results are compared with the exact solutions found in the limits of d --> infinity and d = 1. (C) 2000 Elsevier Science B.V. All rights reserved.