Abstract
The energy spectrum of the quantum Klein-Gordon (KG) lattice is computed numerically for model parameters relevant to optical phonon spectra. A pairing of phonon states is found when nonlinearity is significant, which agrees with other studies on different quantum lattice models (Agranovich V. M., in Spectroscopy and Excitation Dynamics of Condensed Molecular Systems, edited by Agranovich V. M. and Hochstrasser R. M. (North-Holland Publishing Company) 1983, pp. 83-138; Eilbeck J. C., Proceedings of the Third Conference Localization and Energy Transfer in Nonlinear Systems, edited by Vazquez L., MacKay R. S. and Zorzano M. P. (World Scientific, Singapore) 2003, p. 177). It results from the lattice anharmonicity, the magnitude of which is quantified by the binding energy of phonon bound states. Our work focuses on the case of weak anharmonicity, i.e., the phonon binding energy is weaker than the single-phonon band width. We find that the phonon pairs dissociate at the center of the lattice Brillouin zone, whereas at the edge the binding energy remains comparable to the width of the single-phonon band. Consequently, a weak nonlinearity is characterized by a pseudogap in the energy spectrum of two-phonon states.