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arXiv · 1605.00062

Generalization of the tensor renormalization group approach to 3-D or higher dimensions

Peiyuan Teng
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Abstract

In this paper, a way of generalizing the tensor renormalization group(TRG) is proposed. Mathematically, the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is discovered. A theoretical contraction framework is therefore proposed. Furthermore, the canonical polyadic decomposition is introduced to tensor network theory. A lowest order numerical verification of this method on the 3-D Ising model is carried out.

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Peiyuan Teng. 2016-04-30. Generalization of the tensor renormalization group approach to 3-D or higher dimensions. https://doi.org/10.1016/j.physa.2016.12.080

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