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Tensor renormalization group study of the three-dimensional SU(2) and SU(3) gauge theories with the reduced tensor network formulation

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arxiv 2406.16763 v3 pith:L7O6QTRB submitted 2024-06-24 hep-lat cond-mat.stat-mechhep-th

Atis Yosprakob , Kouichi Okunishi This is my paper · ORCID
classification hep-latcond-mat.stat-mechhep-th
keywords gaugetensorformulationgrouprenormalizationtheoriesarmillaryaverage
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We perform a tensor renormalization group simulation of non-Abelian gauge theory in three dimensions using a formulation based on the `armillary sphere.' In this formulation, matrix indices are completely traced out, eliminating the degeneracy in the singular value spectrum of the initial tensor. We demonstrate the usefulness of this technique by computing the average plaquette at zero temperature and the Polyakov loop susceptibility at finite temperatures for 2+1D SU(2) and SU(3) gauge theories. The deconfinement transition is identified for both gauge groups, with the SU(2) case being consistent with previous Monte Carlo results.

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Cited by 3 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. 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...

  3. 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.

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