RELAXATION IN S=1 2 QUANTUM SPIN CHAINS - THE ROLE OF 2ND NEIGHBOR INTERACTIONS/

Most of the existing dynamical studies in one dimension on magnetic in sulators have considered the simplest spin models with nearest-neighbo r interactions. In real systems, however, it is possible that longer r ange interactions are not entirely negligible. It is expected that the inclusion of next-nearest-neighbor interactions between spins in one- dimensional spin models will introduce a multitude of new frequencies in addition to the ones already present in the dynamics that arises du e to nearest-neighbor interactions. We first present an exact solution for the dynamical ax-spin-pair correlations in an Ising chain with bo th nearest- and next-nearest-neighbor interactions to confirm our expe ctation. We next show, via an approximate analytical calculation, that the dynamical zz-spin-pair correlations in the next-nearest-neighbor transverse Ising chain when plotted as a function of time is noticeabl y different with respect to the exactly solvable nearest-neighbor tran sverse Ising chain at T-->infinity when the next-nearest-neighbor inte raction is >1/2 of the magnitude of the nearest-neighbor interaction. The effects could be fairly subtle in the time domain representation a nd in the spectral function when these additional interactions are wea k (i.e., <1/2 of the nearest-neighbor interaction magnitude). The gene ral conclusions reached in this work are expected to be valid for othe r simple quantum spin models such as the XY and XXZ models in one dime nsion.