Plaquette Renormalization Scheme for Tensor Network States

Details Plaquette Renormalization Scheme for Tensor Network States Plaquette Renormalization Scheme for Tensor Network States

2009-01-02

arxiv.org/abs/0901.0214v3

Phys. Rev. E 83, 056703 (2011)

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, 7 figures

Scientific paper

10.1103/PhysRevE.83.056703

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.

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