Renormalization group on a triad network

2019/12/05 by Kadoh, Daisuke, Nakayama, Katsumasa · 4 citations
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.1912.02414

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(D⁶) computational cost in any d dimension (d ≥ 2), where D is the truncated bond dimension of tensors. Although it is reduced to O(D⁵) 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 Ds with reasonable errors.

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• Phase structure of (3+1)-dimensional dense two-color QCD at T=0 in the strong coupling limit with tensor renormalization group
• Tensor renormalization group approach to entanglement entropy
• Triad representation for the anisotropic tensor renormalization group in four dimensions

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