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

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• 作者：Peiyuan Teng ^{teng.73@osu.edu}
• 关键词：Tensor renormalization group ; Truncation sequence ; Tessellation ; Canonical polyadic decomposition ; Ising model
• 刊名：Physica A: Statistical Mechanics and its Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：472
• 期：Complete
• 页码：117-135
• 全文大小：2217 K
• 卷排序：472

文摘

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.