  Tensor network techniques have proved to be powerful tools that can be
employed to explore the large scale dynamics of lattice systems. Nonetheless,
the redundancy of degrees of freedom in lattice gauge theories (and related
models) poses a challenge for standard tensor network algorithms. We
accommodate for such systems by introducing an additional structure decorating
the tensor network. This allows to explicitly preserve the gauge symmetry of
the system under coarse graining and straightforwardly interpret the fixed
point tensors. We propose and test (for models with finite Abelian groups) a
coarse graining algorithm for lattice gauge theories based on decorated tensor
networks. We also point out that decorated tensor networks are applicable to
other models as well, where they provide the advantage to give immediate access
to certain expectation values and correlation functions.
