Pith. sign in

REVIEW 5 cited by

Renormalization group on a triad network

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1912.02414 v1 pith:CCELRBBT submitted 2019-12-05 hep-lat cond-mat.stat-mechhep-th

classification hep-latcond-mat.stat-mechhep-th
keywords costdimensionnetworkrenormalizationtensortensorsalthoughbecause
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We propose a new renormalization scheme of tensor networks made only of third order tensors. The isometry used for coarse-graining the network can be prepared at an $O(D^6)$ computational cost in any $d$ dimension ($d \ge 2$), where $D$ is the truncated bond dimension of tensors. Although it is reduced to $O(D^5)$ if a randomized singular value decomposition is employed, the total cost is $O(D^{d+3})$ because the contraction part for creating a renormalized tensor with isometries has $D^{d+3}$ multiplications. We test our method in three dimensional Ising model and find that the numerical results are obtained for large $D$s with reasonable errors.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 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

    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.

  2. 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.

  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. Initial tensor construction for the tensor renormalization group

    hep-lat 2025-01 conditional novelty 4.0 of 10

    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...

  5. Toward tensor renormalization group study of lattice QCD

    hep-lat 2025-01 conditional novelty 3.0 of 10

    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.

Pith tools