  Cluster expansions for the exponential of local operators are constructed
using tensor networks. In contrast to other approaches, the cluster expansion
does not break any spatial or internal symmetries and exhibits a very
favourable prefactor to the error scaling versus bond dimension. This is
illustrated by time evolving a matrix product state using very large time
steps, and by constructing a novel robust algorithm for finding ground states
of 2-dimensional Hamiltonians using projected entangled pair states as fixed
points of 2-dimensional transfer matrices.
