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arXiv · 1809.08030

Tensor Renormalization Group Algorithms with a Projective Truncation Method

Yoshifumi Nakamura·Hideaki Oba·Shinji Takeda
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Abstract

We apply the projective truncation technique to the tensor renormalization group (TRG) algorithm in order to reduce the computational cost from $O(χ^6)$ to $O(χ^5)$, where $χ$ is the bond dimension, and propose three kinds of algorithms for demonstration. On the other hand, the technique causes a systematic error due to the incompleteness of a projector composed of isometries, and in addition requires iteration steps to determine the isometries. Nevertheless, we find that the accuracy of the free energy for the Ising model on a square lattice is recovered to the level of TRG with a few iteration steps even at the critical temperature for $χ$ = 32, 48, and 64.

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Yoshifumi Nakamura, Hideaki Oba, Shinji Takeda. 2019-04-02. Tensor Renormalization Group Algorithms with a Projective Truncation Method. https://doi.org/10.1103/physrevb.99.155101

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