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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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Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method

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    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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    hep-lat 2026-01 conditional novelty 6.0 of 10

    In strong-coupling lattice QCD at Nτ=8, the chiral and nuclear transition endpoints coincide at m_c≈2.06, and a first-order transition persists at m=2.07 on a 1024^4 zero-temperature lattice.

  3. Tensor renormalization group approach to entanglement entropy

    hep-lat 2025-09 conditional novelty 6.0 of 10

    A tensor renormalization group algorithm computes entanglement entropy for arbitrary single-interval subsystems and reproduces c=0.49997(8) in the 2D Ising model.

  4. Applying the Triad network representation to four-dimensional ATRG method

    hep-lat 2024-12 conditional novelty 5.0 of 10

    Triad-ATRG applies the triad and MDTRG decomposition to four-dimensional ATRG, reducing the contraction cost to O(r^2 χ^7) while reproducing ATRG free energies and transition temperatures.

  5. Initial tensor construction for the tensor renormalization group

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    A delta-function index-shifting algorithm builds locally connected initial tensors for the tensor renormalization group from arbitrary Boltzmann factors, and boundary-style squeezers remove the initial-tensor dependen...

  6. Toward tensor renormalization group study of lattice QCD

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    Tensor renormalization group methods for multi-flavor and non-Abelian gauge theories are summarized with 2D Z2 and 3D SU(2) and SU(3) proof-of-principle results.

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