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

TL;DR

This paper derives an exact density matrix for the kink ground state of the ferromagnetic XXZ chain, enabling precise calculation of correlation functions, decay behaviors, and entanglement entropy, revealing unique properties of the state.

Contribution

It provides the first exact expression for the density matrix of the kink ground state in the XXZ chain, allowing detailed analysis of correlation decay and entanglement.

Findings

Spin-spin correlations decay exponentially with distance.

String formation probabilities decay Gaussianly for large strings.

Entanglement entropy shows non-uniform behavior due to broken translational symmetry.

Abstract

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.