(a).[]{data-label="figXXZ_2"}](xxzspin10b.eps "fig:"){width="0.7\linewidth"} ![(color online) (a) Sublattice components of the local magnetization $m$, (b) amplitude of the local order parameters $M_{xy}$ and $M_z$, (c) total antiferromagnetic order parameter $M_t$ and (d) GE per lattice site ${\mathcal E}(\Delta)$ as a function of anisotropy parameter $\Delta$ for the 2D spin-$1$ XXZ model. Values of the iPEPS truncation dimension $D$ are as indicated, with $D=9$ for (a).[]{data-label="figXXZ_2"}](xxzspin10c.eps "fig:"){width="0.7\linewidth"} ![(color online) (a) Sublattice components of the local magnetization $m$, (b) amplitude of the local order parameters $M_{xy}$ and $M_z$, (c) total antiferromagnetic order parameter $M_t$ and (d) GE per lattice site ${\mathcal E}(\Delta)$ as a function of anisotropy parameter $\Delta$ for the 2D spin-$1$ XXZ model. Values of the iPEPS truncation dimension $D$ are as indicated, with $D=9$ for (a).[]{data-label="figXXZ_2"}](xxzspin10d.eps "fig:"){width="0.7\linewidth"}

summary and discussion
======================

We have demonstrated how to efficiently compute the GE of 2D quantum models defined on the infinite square lattice, by optimizing over all possible separable states, in the context of the tensor network algorithm based on the iPEPS representation. Our results, in line with previous studies [@hl; @gehlw; @thesis; @roman; @z3pott], demonstrate that GE is able to detect continuous quantum phase transitions and factorized fields for different 2D quantum systems. 