  The exact expression for the density matrix of the kink ground state of the
ferromagnetic XXZ chain is obtained. Utilizing this, we exactly calculate
various correlation functions such as the longitudinal and transverse spin-spin
correlation functions, and the ferromagnetic and antiferromagnetic string
formation probabilities. The asymptotic behaviors of these correlation
functions are also analyzed. As a consequence, we find that the spin-spin
correlation functions decay exponentially for large distances, while the string
formation probabilities exhibit Gaussian decay for large strings. We also
evaluate the entanglement entropy, which shows interesting behaviors due to the
lack of the translational invariance of the state.
