degenerate ground states and identify both continuous and discontinuous quantum phase transitions.

To address this issue, we improve a systematic method [@gehlw] to efficiently compute the GE per lattice site for 2D quantum many-body lattice systems in the context of tensor network algorithms based on an infinite projected entangled pair state (iPEPS) representation. This method is used to evaluate the GE per lattice site for a number of distinct models defined on the infinite square lattice. These models are (i) the quantum Ising model in a transverse field, (ii) the $q$-state quantum Potts model with $q=3, 4$ and $5$, (iii) the spin-$\frac12$ antiferromagnetic XXX model in an external magnetic field, (iv) the spin-$\frac12$ antiferromagnetic XYX model in an external magnetic field, and (v) the spin-$1$ XXZ model. By comparing the behavior of the local order parameters and the GE per site for the different models, it is seen that GE can detect both continuous and discontinuous quantum phase transitions. However, we observe that the continuity of the GE per site does not necessarily match with the continuity of local order parameters.

This paper is arranged as follows. The definition of GE is given in Section II. Results using the GE 