Dynamics of the one-dimensional Heisenberg model and optical absorption of spinons in cuprate antiferromagnetic chains

We use numerical and analytical results to construct a simple ansatz for the energy dynamical correlation function of the one-dimensional antiferromagnetic Heisenberg model. This is applied to compute the phonon-assisted absorption spectra of magnetic excitations (spinons) in quasi-one-dimensional spin-1/2 insulators and shown to reproduce very well recent infrared measurements in ${\mathrm{Sr}}_2$ ${\mathrm{CuO}}_3$.