Anisotropic tensor renormalization group
Anisotropic tensor renormalization group
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DOI：
10.1103/physrevb.102.054432
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发表时间：
2019-06
影响因子：
3.7
通讯作者：
Daiki Adachi;T. Okubo;S. Todo
中科院分区：
文献类型：
--
作者：
Daiki Adachi;T. Okubo;S. Todo
提出了一种新的张量重整化群算法--各向异性张量重整化群算法（ATRG），用于任意维格点模型。所提出的方法与高阶张量重整化群（HOTRG）算法共享相同的通用性，即，它在重整化之后保持了晶格拓扑。与HOTRG相比，我们的方法的计算成本和内存占用都大大减少，特别是在更高的维度上，通过在奇异值分解后以各向异性的方式重新归一化张量。我们证明了ATRG的能力，正方形晶格和简单立方晶格伊辛模型。虽然本方法的精度下降时相比，HOTRG相同的键尺寸，精度与固定的计算时间大大提高，由于计算成本的急剧下降。
We propose a new tensor renormalization group algorithm, Anisotropic Tensor Renormalization Group (ATRG), for lattice models in arbitrary dimensions. The proposed method shares the same versatility with the Higher-Order Tensor Renormalization Group (HOTRG) algorithm, i.e., it preserves the lattice topology after the renormalization. In comparison with HOTRG, both of the computation cost and the memory footprint of our method are drastically reduced, especially in higher dimensions, by renormalizing tensors in an anisotropic way after the singular value decomposition. We demonstrate the ability of ATRG for the square lattice and the simple cubic lattice Ising models. Although the accuracy of the present method degrades when compared with HOTRG of the same bond dimension, the accuracy with fixed computation time is improved greatly due to the drastic reduction of the computation cost.