Bond-weighted tensor renormalization group
Bond-weighted tensor renormalization group
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DOI：
10.1103/physrevb.105.l060402
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发表时间：
2020-11
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
本文提出了一种改进的张量重整化群（TRG）算法--键权TRG（BTRG）。在BTRG中，我们通过在张量网络的边缘上引入键权来推广传统的TRG。我们发现，BTRG优于传统的TRG和高阶张量重整化群具有相同的键维数，而它的计算时间几乎是相同的TRG。此外，BTRG可以有非平凡的不动点张量在一个最佳的超参数。我们证明了BTRG得到的奇异值谱在二维伊辛模型的临界点处的重整化过程下是不变的。这一性质表明BTRG在保持张量尺度不变结构的同时，能够高精度地进行张量收缩。
We propose an improved tensor renormalization group (TRG) algorithm, the bond-weighted TRG (BTRG). In BTRG, we generalize the conventional TRG by introducing bond weights on the edges of the tensor network. We show that BTRG outperforms the conventional TRG and the higher-order tensor renormalization group with the same bond dimension, while its computation time is almost the same as that of TRG. Furthermore, BTRG can have non-trivial fixed-point tensors at an optimal hyperparameter. We demonstrate that the singular value spectrum obtained by BTRG is invariant under the renormalization procedure in the case of the two-dimensional Ising model at the critical point. This property indicates that BTRG performs the tensor contraction with high accuracy while keeping the scale-invariant structure of tensors.