Density matrix for the kink ground state of the ferromagnetic XXZ chain

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.

💡 Research Summary

The paper addresses a long‑standing gap in the analytical understanding of non‑translationally invariant states in the one‑dimensional ferromagnetic XXZ spin‑½ chain. While the Bethe Ansatz provides exact eigenstates for the homogeneous ground state, it does not directly yield the density matrix for a domain‑wall (kink) configuration, which consists of two oppositely polarized ferromagnetic domains separated by a single defect. The authors overcome this obstacle by constructing an explicit matrix‑product representation of the kink ground state and then deriving its full reduced density matrix ρ = |Ψ_kink⟩⟨Ψ_kink|.

The construction starts from the Hamiltonian
H = −∑_{j}