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Anisotropic Tensor Renormalization Group

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arxiv 1906.02007 v2 pith:UKMISIA5 submitted 2019-06-05 cond-mat.stat-mech cond-mat.str-elphysics.comp-phquant-ph

Daiki Adachi , Tsuyoshi Okubo , Synge Todo This is my paper · ORCID
classification cond-mat.stat-mechcond-mat.str-elphysics.comp-phquant-ph
keywords renormalizationgrouplatticetensoranisotropiccomputationhotrgmethod
verification ladder T0 review T1 audit T2 compute T3 formal
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We propose a new tensor renormalization group algorithm, Anisotropic Tensor Renormalization Group (ATRG), for lattice models in arbitrary dimensions. The proposed method shares the same versatility with the Higher-Order Tensor Renormalization Group (HOTRG) algorithm, i.e., it preserves the lattice topology after the renormalization. In comparison with HOTRG, both of the computation cost and the memory footprint of our method are drastically reduced, especially in higher dimensions, by renormalizing tensors in an anisotropic way after the singular value decomposition. We demonstrate the ability of ATRG for the square lattice and the simple cubic lattice Ising models. Although the accuracy of the present method degrades when compared with HOTRG of the same bond dimension, the accuracy with fixed computation time is improved greatly due to the drastic reduction of the computation cost.

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Cited by 5 Pith papers

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