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We study the realization of anyon-permuting symmetries of topological phaseson the lattice using tensor networks. Working on the virtual level of aprojected entangled pair state, we find matrix product operators (MPOs) thatrealize all unitary topological symmetries for the toric and color codes. Theseoperators act as domain walls that enact the symmetry transformation on anyonsas they cross. By considering open boundary conditions for these domain wallMPOs, we show how to introduce symmetry twists and defect lines into the state.

Tensor Networks with a Twist: Anyon-permuting domain walls and defects in PEPS