Global optimization of tensor renormalization group using the corner transfer matrix
Global optimization of tensor renormalization group using the corner transfer matrix
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DOI：
10.1103/physrevb.103.045131
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发表时间：
2020-09
影响因子：
3.7
通讯作者：
Satoshi Morita;N. Kawashima
中科院分区：
文献类型：
--
作者：
Satoshi Morita;N. Kawashima
提出了一种基于角点转移矩阵的全局优化张量网络重正化算法。由于角点转移矩阵重整化群方法是对环境进行更新，因此不需要进行前向-后向迭代，而前向-后向迭代是其他全局优化方法中耗时的部分。此外，提出了一种进一步的近似方法，降低了粗粒度张量计算的收缩计算成本。我们的算法在二维尺度的计算时间为键维的六次方，而高阶张量重整化群和高阶二阶重整化群方法具有七次方。我们进行基准计算的伊辛模型上的正方形格子，并表明，所提出的算法的解决方案的时间比其他方法更快。
A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration is unnecessary, which is a time-consuming part of other methods with global optimization. In addition, a further approximation reducing the order of the computational cost of contraction for the calculation of the coarse-grained tensor is proposed. The computational time of our algorithm in two dimensions scales as the sixth power of the bond dimension, while the higher-order tensor renormalization group and the higher-order second renormalization group methods have the seventh power. We perform benchmark calculations in the Ising model on the square lattice and show that the time-to-solution of the proposed algorithm is faster than that of other methods.