Phonon dispersion relations in a two-dimensional electron–lattice system at non-zero temperatures

Phonon dispersion relations in a two-dimensional electron–lattice system described by a two-dimensional square-lattice version of Su–Shrieffer–Heegerʹs model and having a half-filled electronic band are numerically studied at non-zero temperatures. When lowering temperature from a region higher than the critical temperature of the Peierls transition, multi-mode phonon softening is confirmed; the softening modes have wave vectors parallel to the nesting vector Q=(π,π) including Q itself. Some preliminary results in the temperature region lower than the critical temperature are also reported.