三元网络上的重整化群
Renormalization group on a triad network
摘要：
本文提出了一种新的仅由三阶张量构成的张量网络的重整化方案。用于粗粒化网络的等距可以在任何$d$维度（$d \ge 2$）中以$O(D^6)$计算成本制备，其中$D$是张量的截断键维度。虽然如果采用随机奇异值分解，它被简化为$O(D^5)$，但总成本是$O(D^{d+3})$，因为用于创建具有等距的重整化张量的收缩部分具有$D^{d+3}$乘法。我们在三维伊辛模型中对我们的方法进行了检验，发现对于大的$D$ s，我们得到了数值结果，误差在合理范围内。
英文摘要：
We propose a new renormalization scheme of tensor networks made only of third order tensors. The isometry used for coarse-graining the network can be prepared at an $O(D^6)$ computational cost in any $d$ dimension ($d \ge 2$), where $D$ is the truncated bond dimension of tensors. Although it is reduced to $O(D^5)$ if a randomized singular value decomposition is employed, the total cost is $O(D^{d+3})$ because the contraction part for creating a renormalized tensor with isometries has $D^{d+3}$ multiplications. We test our method in three dimensional Ising model and find that the numerical results are obtained for large $D$s with reasonable errors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
