Two-dimensional Peierls transition with multimode lattice distortions

Peierls transition in a square lattice electron-lattice system described by a two-dimensional version of Su, Schrieffer and Heeger's model with a half-filled electronic band is numerically analyzed. The Peierls phase accompanied by multimode distortions, where lattice distortions not only with the nesting vector Q = (π,π) but also with those wave vectors parallel to Q are coexisting, is found to be the lowest Free energy state even at finite temperatures. In contrast to the Peierls phase involving only the distortion with the nesting vector, there is no gapless region along the Fermi line.