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2009

Plaquette Renormalization Scheme for Tensor Network States

Wang, Ling, Kao, Ying-Jer, Sandvik, Anders W.

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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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S. R. White, Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
S. Östlund and S. Rommer, Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
H. Rieger and N. Kawashima, Eur. Phys. J. B 9
1999
Earlier work this paper cites.
H. Takasaki, T. Hikihara, and T. Nishino, J. Phys. Soc. Jpn. 68
2000
Earlier work this paper cites.
A. W. Sandvik, Phys. Rev. E 68
2003
Earlier work this paper cites.
F. Verstraete, D. Porras, J. I. Cirac, Phys. Rev. Lett. 93
2004
Earlier work this paper cites.
U. Schollwöck, Rev. Mod. Phys. 77
2005
Earlier work this paper cites.

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