论文标题
使用角传递矩阵对张量重归其化组的全局优化
Global optimization of tensor renormalization group using the corner transfer matrix
论文作者
论文摘要
提出了基于角传递矩阵的全局优化的张量网络重归其化算法。由于环境通过角传输矩阵重归于分组方法更新，因此前进迭代是不必要的，这是具有全局优化的其他方法的耗时部分。此外，提出了进一步的近似，以减少收缩成本的计算计算量的顺序。我们的算法的计算时间二维尺度是键尺寸的第六次功率，而高阶张量重量化组和高阶第二重新归一化组方法具有第七次功率。我们在平方晶格上的ISING模型中执行基准计算，并表明所提出的算法的时间比其他方法要快。
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.
