Competition of different types of electron-lattice coupling in 2D Peierls transition

The stability of the multimode Peierls (MMP) state, which has been predicted for the 2D square-lattice electron system with the Su-Schrieffer-Heeger (SSH) type electron-lattice (e-l) coupling and with a half-filled electronic band, is discussed in the presence of a dilation-type e-l interaction. To understand the role of the latter interaction, the ground state for the model with only the latter interaction is numerically investigated for the 1D chain and the 2D square lattice. The results indicate that this interaction favors a phase separation into two regions, one with sites doubly occupied by electrons and the other with sites having no electron. Detailed numerical analyses show that the MMP state in the 2D system can survive even in the presence of the dilation-type interaction as long as its coupling strength is weak compared to that of the SSH-type interaction.