Multipartite entanglement and criticality in two-dimensional XXZ model

We investigate the multipartite entanglement and the trace distance for the two-dimensional XXZ anisotropic spin-12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{2}$$\end{document} lattice and observe that the quantum phase transition is independent of the chosen quantifier. It is found that for a many-body quantum system the multipartite entanglement is more robust than the bipartite entanglement due to the monogamy property. Quantum renormalization group technique is used to solve the two-dimensional XXZ model that results in only one unstable fixed point (the critical point). In thermodynamic limit, the quantum phase transition point coincides with the critical point. After sufficient iterations of the quantum renormalization group, we observe two different saturated values of the quantifiers that represent two separate phases, the spin fluid phase and the Néel phase. The first derivative and the scaling behavior of the renormalized entanglement quantifiers are computed. At phase transition point, the non-analytic behavior of the first derivative of the two quantifiers as a function of lattice size is examined and it is found that the universal finite-size scaling law is obeyed. Furthermore, we observe that at the critical point the scaling exponent for the multipartite entanglement and the trace distance can describe the correlation length of the model.