Local lattice distortion in high-T_c cuprates

The dynamical local lattice distortion in the CuO₂ plane of the cuprate high-temperature superconductors is investigated with the numerical diagonalization study for finite clusters of t-J model. It is found that the in-plane vibrations of the oxygens play an important role in the formation of some static orders like CDW and SDW through the polaronic self localization effect. The 1/8 problem is also discussed based on the present result.