Optical conductivity in the t-J Holstein model

Using a recently developed numerical method we compute charge stiffness and optical conductivity of the t-J model coupled to optical phonons. Coherent hole motion is most strongly influenced by the electron-phonon coupling within the physically relevant regime of the exchange interaction. We find unusual nonmonotonous dependence of the charge stiffness as a function of the exchange coupling near the crossover to the strong electron-phonon coupling regime. Optical conductivity in this regime shows a two-peak structure. The low-frequency peak represents local magnetic excitation, attached to the hole, while the higher-frequency peak corresponds to the mid-infrared band that originates from coupling to spin-wave excitations, broadened and renormalized by phonon excitations. We observe no separate peak at or slightly above the phonon frequency. This finding suggests that in the framework of the t-J Holstein model the two-peak structure seen in recent optical measurements is due to magnetic excitations coupled to lattice degrees of freedom via doped charge carriers.