breaking, indicated from the random-like magnetization of sublattices as shown in Fig. \[figXXZ\_2\](a). For $\Delta>1$, the phase is characterized by the antiferromagnetic order parameter $M_z$ along the easy axis, with doubly degenerate ground states corresponding to the spin-flip (or one-site translational invariant) $Z_2$ symmetry breaking. These order parameters are shown in Fig. \[figXXZ\_2\](b). For each truncation dimension, a distinct jump is detected at $\Delta=1$, indicating the phase transition is possibly discontinuous. The total antiferromagnetic order parameter $
M_{t}=\sqrt{\langle \frac12 (S_x^A-S_x^B)\rangle^2+\langle \frac12 (S_y^A-S_y^B)\rangle^2
+\langle \frac12 (S_z^A-S_z^B)\rangle^2}
$ is shown in Fig. \[figXXZ\_2\](c). It varies continuously.

For comparison we also consider the GE per site for this model. The GE per site is seen to take the same value for all of the degenerate ground states. As shown in Fig. \[figXXZ\_2\](d), the GE is continuous with a well defined cusp at the point $\Delta=1$, while the local order parameters in Fig. \[figXXZ\_2\](b) are discontinuous at $\Delta=1$. This behavior is similar to that observed in the previous subsection for the 2D spin-$\frac12$ XYX model with fixed magnetic field $h$.

![(color online) Single-copy entanglement (a) $S_1(\Delta)$ and (b) $S_2(\Delta)$ as a function of the anisotropy parameter $\Delta$ for the 2D spin-$1$ XXZ model with 