Finite-size effects on the optical conductivity of a half-filled Hubbard ring

We use the Bethe-ansatz equations to calculate the total and zero-frequency spectral weight in the optical conductivity of the half-filled one-dimensional Hubbard model as a function of the lattice size L and the on-site repulsion U. The zero-frequency spectral weight D scales as L1/2exp(-L/) as L. Near U=0, varies as the inverse of the Lieb-Wu charge gap. In the strongly correlated regime (Ut), -1=ln(U/t)-1.48. $D is negative when L is a multiple of 4, corresponding to a negative inductance. We give a physical explanation of our results in terms of a simple model of ring exchange. The finite-size corrections to the total spectral weight scale as L-2. We discuss the implications of our results for exact diagonalization calculations of the optical conductivity.