Tensor network approach to two-dimensional Yang?Mills theories
Tensor network approach to two-dimensional Yang?Mills theories
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二维杨?米尔斯理论的张量网络方法
DOI：
10.1093/ptep/ptab143
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发表时间：
2021
影响因子：
3.5
通讯作者：
Matsumoto Nobuyuki
中科院分区：
文献类型：
--
作者：
Fukuma Masafumi;Kadoh Daisuke;Matsumoto Nobuyuki
本文提出了具有任意紧规范群的二维Yang-Mills理论的一种新的张量网络表示。在该方法中，张量指标直接由群元素给出，不直接使用字符展开。我们将张量重整化群方法应用到su(2)和su(3)的张量网络中，得到了准确的自由能密度和能量密度。我们还证明了张量的奇异值分解具有群论结构，并且可以与特征展开相关联。
We propose a novel tensor network representation for two-dimensional Yang–Mills theories with arbitrary compact gauge groups. In this method, tensor indices are given directly by group elements with no direct use of the character expansion. We apply the tensor renormalization group method to this tensor network forSU(2) andSU(3), and find that the free energy density and the energy density are accurately evaluated. We also show that the singular value decomposition of a tensor has a group-theoretic structure and can be associated with the character expansion.