Next-nearest-neighbor spin-spin and chiral-spin correlation functions in generalized XXX chain

TL;DR

This paper introduces a straightforward analytical method to compute next-nearest-neighbor and chiral-spin correlation functions in the inhomogeneous XXX spin chain, providing explicit formulas and extending to related models.

Contribution

It presents a new simple technique for calculating complex correlation functions in the XXX model, including an exact expression for the chiral-spin order parameter.

Findings

Derived an exact formula for the chiral-spin order parameter as a function of model parameter ω.

Calculated the next-nearest-neighbor spin-spin correlation function analytically.

Reproduced known results in the limit ω -> 0 for the standard Heisenberg chain.

Abstract

We develop a simple technique for calculation of next to nearest neighbor spin-spin and chiral-spin correlation functions in inhomogeneous XXX model. Exact expression of the chiral-spin order parameter as a function of the model parameter, $\omega$, is analytically found. Using the same method we also calculate the next to nearest neighbor spin-spin correlation function. In the limit $\omega -> 0$ 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 XXZ model.