Plaquette renormalization scheme for tensor network states

Author(s): L. Wang, Y.-J. Kao, A. W. Sandvik

Journal: Phys. Rev. E

Volume: 83

Page(s): 5

Year: 2011

DOI Number: 10.1103/PhysRevE.83.056703

Link: Link to publication


We present a method for contracting a square-lattice tensor network in two dimensions based on auxiliary tensors accomplishing successive truncations (renormalization) of eight-index tensors for 2×2 plaquettes into four-index tensors. Since all approximations are done on the wave function (which also can be interpreted in terms of different kinds of tensor networks), 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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