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2019

Renormalization group on a triad network

Kadoh, Daisuke, Nakayama, Katsumasa

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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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