per lattice site as a marker of quantum phase transitions in the various 2D quantum models on the infinite square lattice are given in Section III using the procedure outlined in Appendices A and B based on the iPEPS representation. Discussion of the results and concluding remarks are given in Section IV.

The geometric entanglement per lattice site
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For a pure quantum state $|\psi\rangle$ with $N$ parties, the GE, as a global measure of the multipartite entanglement, quantifies the deviation from the closest separable state $|\phi\rangle$. For a spin system each party could be a single spin but could also be a block of contiguous spins. The GE $E(|\psi\rangle)$ for an $N$-partite quantum state $|\psi\rangle$ is expressed as [@review; @hba; @tcw] $$E(|\psi\rangle)=-\log_2{\Lambda_{{\rm max}}^{2}}, \label{def}$$ where $\Lambda_{\rm max}$ is the maximum fidelity between $|\psi\rangle$ and all possible separable (unentangled) and normalized states $|\phi\rangle$, with $$\Lambda_{{\rm max} }={\rm \max_{|\phi\rangle }} \; |\langle\psi|\phi\rangle|.$$ The GE per party ${\mathcal E}_{N}(|\psi\rangle)$ is then defined as $${\mathcal E}_{N}(|\psi\rangle)=N^{-1}E(|\psi\rangle).$$ It corresponds to the maximum fidelity per party $\lambda^{{\rm
max}}_{N}$, where $$\lambda^{{\rm max}}_{N}=\sqrt[N]{{\Lambda_{{\rm max}}}},$$ or equivalently, $${\mathcal E}_{N}(|\psi\rangle)=-\log_2{{(\lambda^{{\rm
max}}_{N})}^{2}}.$$ The relation (\[def\]) is analogous to the relation between the free energy and the partition function. Note that 