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.
@article{arxiv.0901.0214,
title = {Plaquette Renormalization Scheme for Tensor Network States},
author = {Ling Wang and Ying-Jer Kao and Anders W. Sandvik},
journal= {arXiv preprint arXiv:0901.0214},
year = {2011}
}