Two-Dimensional Tensor Product Variational Formulation.

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  • Nishino Tomotoshi
    Department of Physics, Graduate School of Science, Kobe University<BR>Kobe 657-8501, Japan
  • Hieida Yasuhiro
    Department of Physics, Graduate School of Science, Kobe University<BR>Kobe 657-8501, Japan
  • Okunishi Kouichi
    Department of Applied Physics, Graduate School of Engineering<BR> Osaka University, Suita 565-0871, Japan Department of Physics, Niigata University, Niigata 950-2181, Japan
  • Maeshima Nobuya
    Department of Physics, Graduate School of Science, Osaka University<BR> Toyonaka 560-0043, Japan
  • Akutsu Yasuhiro
    Department of Physics, Graduate School of Science, Osaka University<BR> Toyonaka 560-0043, Japan
  • Gendiar Andrej
    Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, SK-842 28 Bratislava, Slovakia

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We propose a numerical self-consistent method for 3D classical lattice models, which optimizes the variational state written as a two-dimensional product of tensors. The variational partition function is calculated using the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The numerical efficiency of the method is exemplified in its application to the 3D Ising model.

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