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arXiv · 1912.02414

Renormalization group on a triad network

Daisuke Kadoh·Katsumasa Nakayama
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Abstract

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.

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Daisuke Kadoh, Katsumasa Nakayama. 2019-12-05. Renormalization group on a triad network. https://arxiv.org/abs/1912.02414

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