Optical conductivity of the half-filled Hubbard chain

We combine well-controlled analytical and numerical methods to determine th e optical conductivity of the one-dimensional Mott-Hubbard insulator at zer o temperature. A dynamical density-matrix renormalization group method prov ides the entire absorption spectrum for all but very small coupling strengt hs. In this limit we calculate the conductivity analytically using exact fi eld-theoretical methods. Above the Lieb-Wu gap the conductivity exhibits a characteristic square-root increase. For small to moderate interactions, a sharp maximum occurs just above the gap. For larger interactions, another w eak feature becomes visible around the middle of the absorption band.