Singularities in Optical Spectra of Quantum Spin Chains

The midinfrared optical absorption spectrum is reported of the one-dimensional Mott insulator S${\mathrm{r}}_2$Cu${\mathrm{O}}_3$. The spectrum has an asymmetric cusplike structure at 0.48 eV and is analyzed in terms of the phonon-assisted absorption in the one-dimensional quantum spin chain model. A good agreement is obtained between experiment and theory, and the exchange energy J is estimated to be $J\approx 0.26$ eV, which is consistent with the magnetic susceptibility measurement.