2D Luttinger liquid behaviors in high-Tc superconductors

The d-p model is reduced to a Hamiltonian that displays the quasi-particles interact with a 2D Luttinger liquid. The Luttinger liquid is composed of the charge density oscillations and spin waves. It is found that the properties such as the high temperature superconductivity, unusual isotope effects and T-linear resistivity can be described well with the Hamiltonian.