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Bond-weighted Tensor Renormalization Group

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arxiv 2011.01679 v1 pith:BNBBKKJU submitted 2020-11-03 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 btrgtensorrenormalizationgroupbondbond-weightedconventionalsame
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We propose an improved tensor renormalization group (TRG) algorithm, the bond-weighted TRG (BTRG). In BTRG, we generalize the conventional TRG by introducing bond weights on the edges of the tensor network. We show that BTRG outperforms the conventional TRG and the higher-order tensor renormalization group with the same bond dimension, while its computation time is almost the same as that of TRG. Furthermore, BTRG can have non-trivial fixed-point tensors at an optimal hyperparameter. We demonstrate that the singular value spectrum obtained by BTRG is invariant under the renormalization procedure in the case of the two-dimensional Ising model at the critical point. This property indicates that BTRG performs the tensor contraction with high accuracy while keeping the scale-invariant structure of tensors.

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Cited by 5 Pith papers

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

  1. Deconfinement from Thermal Tensor Networks: Universal CFT signature in (2+1)-dimensional $\mathbb{Z}_N$ lattice gauge theory

    hep-th 2026-02 conditional novelty 7.0 of 10

    Tensor-network contraction of finite-temperature Z_N gauge theory yields central charges and scaling dimensions consistent with Svetitsky–Yaffe universality for N=2,3,5, including a U(1)-symmetric BKT phase for N=5, a...

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

    hep-lat 2026-02 conditional novelty 7.0 of 10

    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.

  3. Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group

    hep-lat 2026-02 conditional novelty 6.0 of 10

    For one-flavor Gross-Neveu-Wilson fermions, the Aoki phase is bounded by c=1/2 Ising critical lines and terminates at strong coupling, while c=1 lines separate topological and trivial insulators.

  4. Tensor renormalization group study of cold and dense QCD in the strong coupling limit

    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.

  5. Phase structure analysis of CP(1) model with $\theta$ term by tensor renormalization group

    hep-lat 2025-02 conditional novelty 6.0 of 10

    Numerical tensor-network results locate a critical point at theta=pi in the 2D CP(1) model, consistent with Haldane's conjecture.

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