Spin, charge, and electronic excitations in cuprate superconductors: Role of the long-range hoppings

The single-particle spectral functions of the t-t'-t''-J model are exactly calculated for a full range of the Brillouin zone by introducing the twisted boundary conditions for a 20-site cluster. By using the spectral functions, we calculate the optical conductivity σ(ω). In the hole-doped system, σ(ω) shows a good agreement with the exact ones based on the linear response theory. On the contrary, σ(ω) in the electron-doped system disagree with the exact ones. This is due to the presence of strong antiferromagnetic correlations induced by the long-range hopping t' and t''