  We present a method for contracting a square-lattice tensor network in two
dimensions, based on auxiliary tensors accomplishing successive truncations
(renormalization) of 8-index tensors for 2 by 2 plaquettes into 4-index
tensors. The scheme is variational, and thus the tensors can be optimized by
minimizing the energy. Test results for the quantum phase transition of the
transverse-field Ising model confirm that even the smallest possible tensors
(two values for each tensor index at each renormalization level) produce much
better results than the simple product (mean-field) state.
