![(color online) Numerical values for the local order parameter $\langle M_{x_1}\rangle$ and the GE per site ${\mathcal E}(\lambda)$ for the 2D quantum $q$-state Potts model for (a) $q=3$, (b) $q=4$ and (c) $q=5$ as a function of the transverse field strength $\lambda$ for the indicated values of the iPEPS truncation dimension $D$. For each case the curves for both the local order parameter and the GE show a discontinuous behavior, indicative of a discontinuous phase transition. []{data-label="fig2"}](q4.eps "fig:"){width="1.0\linewidth"} ![(color online) Numerical values for the local order parameter $\langle M_{x_1}\rangle$ and the GE per site ${\mathcal E}(\lambda)$ for the 2D quantum $q$-state Potts model for (a) $q=3$, (b) $q=4$ and (c) $q=5$ as a function of the transverse field strength $\lambda$ for the indicated values of the iPEPS truncation dimension $D$. For each case the curves for both the local order parameter and the GE show a discontinuous behavior, indicative of a discontinuous phase transition. []{data-label="fig2"}](q5.eps "fig:"){width="1.0\linewidth"}

Denoting the phase transition point by $\lambda_c$ we expect to detect $q$-degenerate ground states for $\lambda<\lambda_c$, corresponding to a $Z_q$ broken symmetry phase. The local order parameter $\langle M_{x,1}\rangle$ can distinguish the different degenerate ground states, but with the same amplitude for each of 