  Due to the unfavorable scaling of tensor network methods with the refinement
parameter M, new approaches are necessary to improve the efficiency of
numerical simulations based on such states in particular for gapless, strongly
entangled systems. In one-dimensional DMRG, the use of Abelian symmetries has
lead to large computational gain. In higher-dimensional tensor networks, this
is associated with significant technical efforts and additional approximations.
We explain a formalism to implement such symmetries in two-dimensional tensor
network states and present benchmark results that confirm the validity of these
approximations in the context of projected entangled-pair state algorithms.
