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arXiv:1912.02414

Renormalization group on a triad network

Daisuke Kadoh, Katsumasa Nakayama

Published Jan 1, 2019• 28 citations
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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.

DOI
10.3204/pubdb-2020-00123

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