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

Peiyuan Teng

Physica A: Statistical Mechanics and its Applications, 2017, vol. 472, issue C, 117-135

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 numerical verification of this method on the 3-D Ising model is carried out.

Keywords: Tensor renormalization group; Truncation sequence; Tessellation; Canonical polyadic decomposition; Ising model (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:472:y:2017:i:c:p:117-135

DOI: 10.1016/j.physa.2016.12.080

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