Spectral function and dynamical spin correlation function in the t-t′-t″-j model

Using exact spectral functions of the t-t′-t″-J model obtained by the exact diagonalization technique, we construct the dynamical spin response function. In the hole-doped system, the spin correlation shows a sand-glass-like behavior qualitatively similar to those observed in neutron scattering experiments. This is only clearly seen in the presence of t′ and t″, implying the importance of the Fermi-arc for the sand-glass behavior. On the other hand, the spin correlation function in the electron-doped system does not display the sand-glass-like behavior but shows a behavior similar to a spin-wave-like excitation observed in experiments.