We present a new strategy for contracting tensor networks in arbitrary
geometries. This method is designed to follow as strictly as possible the
renormalization group philosophy, by first contracting tensors in an exact way
and, then, performing a controlled truncation of the resulting tensor. We
benchmark this approximation procedure in two dimensions against an exact
contraction. We then apply the same idea to a three dimensional system. The
underlying rational for emphasizing the exact coarse graining renormalization
group step prior to truncation is related to monogamy of entanglement.Comment: 5 pages, 8 figure