  We simulate a zero-temperature pure $\mathbb{Z}_3$ Lattice Gauge Theory in
2+1 dimensions by using an iPEPS (Infinite Projected Entangled-Pair State)
ansatz for the ground state. Our results are therefore directly valid in the
thermodynamic limit. They clearly show two distinct phases separated by a phase
transition. We introduce an update strategy that enables plaquette terms and
Gauss-law constraints to be applied as sequences of two-body operators. This
allows the use of the most up-to-date iPEPS algorithms. From the calculation of
spatial Wilson loops we are able to prove the existence of a confined phase. We
show that with relatively low computational cost it is possible to reproduce
crucial features of gauge theories. We expect that the strategy allows the
extension of iPEPS studies to more general LGTs.
