  We use Projected Entangled Pair States (PEPS) to study topological quantum
phase transitions. The local description of topological order in the PEPS
formalism allows us to set up order parameters which measure condensation and
deconfinement of anyons, and serve as a substitute for conventional order
parameters. We apply these order parameters, together with anyon-anyon
correlation functions and some further probes, to characterize topological
phases and phase transitions within a family of models based on a $\mathbb Z_4$
symmetry, which contains $\mathbb Z_4$ quantum double, toric code, double
semion, and trivial phases. We find a diverse phase diagram which exhibits a
variety of different phase transitions of both first and second order which we
comprehensively characterize, including direct transitions between the toric
code and the double semion phase.
