论文标题
键加权张量重归其化组
Bond-weighted Tensor Renormalization Group
论文作者
论文摘要
我们提出了一个改进的张量重归其化组（TRG）算法，即键加权TRG（BTRG）。在BTRG中，我们通过在张量网络的边缘引入键重量来推广常规TRG。我们表明，BTRG的表现优于传统的TRG和具有相同键尺寸的高阶张量重量化组，而其计算时间几乎与TRG相同。此外，BTRG可以在最佳的高参数下具有非平凡的定点张量。我们证明，在临界点的二维ISING模型的情况下，BTRG获得的奇异值光谱是不变的。该特性表明BTRG以高精度执行张量收缩，同时保持张量的规模不变结构。
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.
