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Tensor Renormalization Group with Randomized Singular Value Decomposition
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Tensor Renormalization Group with Randomized Singular Value Decomposition
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An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square lattice, its computational complexity and memory usage are proportional to the fifth and the third power of the bond dimension, respectively, whereas those of the conventional implementation are of the sixth and the fourth power. The oversampling parameter larger than the bond dimension is sufficient to reproduce the same result as full singular value decomposition even at the critical point of the two-dimensional Ising model.
Forward citations
Cited by 1 Pith paper
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Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method
Forward-mode AD for TRG is derived with (k+1)(k+2)/2 cost scaling, linked to impurity methods, and tested on the 2D/3D Ising model for energy, specific heat, and critical exponents.
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