Next-nearest-neighbor spin-spin and chiral-spin correlation functions in a generalizedXXXchain

Abstract

We develop a simple technique for calculation of next-to-nearest-neighbor spin-spin and chiral-spin correlation functions in an inhomogeneous $XXX$ model. Exact expression of the chiral-spin order parameter as a function of the model parameter, $\ensuremath{\omega}$, is analytically found. Using the same method we also calculate the next-to-nearest-neighbor spin-spin correlation function. In the limit $\ensuremath{\omega}\ensuremath{\rightarrow}0$ it reproduces the known result for the vacuum expectation value of the next-to-nearest-neighbor spins in the standard Heisenberg spin chain. The technique is simple and can be extended for calculation of next-to-next-to-nearest-neighbor correlation functions as well as for calculation of correlation functions in the $XXZ$ model.