An alternative swapping-bonds step lowers the bottleneck cost of ATRG from O(chi^(2d+1)) to O(chi^max(d+3,7)) and the memory from O(chi^(2d)) to O(chi^max(d+1,6)), with matching 4D Ising results.
Then, in step (f), G and H are contracted to obtain a coarse- grained tensor T′, T′ Ω′ 0Ω′ 1x0x2 = ∑ x1 GΩ′ 0x0x1HΩ′ 1x1x2
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Cost Reduction of Swapping Bonds Part in Anisotropic Tensor Renormalization Group
An alternative swapping-bonds step lowers the bottleneck cost of ATRG from O(chi^(2d+1)) to O(chi^max(d+3,7)) and the memory from O(chi^(2d)) to O(chi^max(d+1,6)), with matching 4D Ising results.