Dynamical correlation functions of the transverse Ising model with next-nearest-neighbor interactions

We investigate the effects of next-nearest-neighbor (NNN) interactions on the dynamics of the one-dimensional spin-1$/$2 transverse Ising model in the high temperature limit. Using exact diagonalization of finite chains, we obtain the time-dependent transverse correlation function and the corresponding spectral density for a tagged spin. Our results for chains of 13 spins with periodic boundary conditions produce results which are valid in the infinite-size limit. In general we find that the NNN coupling produces slower dynamics accompanied by an enhancement of the central mode behavior. Even in the case of a strong transverse field, if the NNN coupling is sufficiently large there is a crossover from collective mode to central mode behavior. We also obtain several recurrants for the continued fraction representation of the relaxation function.