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Doubling of Entanglement Spectrum in Tensor Renormalization Group

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arxiv 1306.6829 v2 pith:XPAOTVCV submitted 2013-06-28 cond-mat.stat-mech quant-ph

Hiroshi Ueda , Kouichi Okunishi , Tomotoshi Nishino This is my paper · ORCID
classification cond-mat.stat-mechquant-ph
keywords entanglementspectrumdoublinghotrggrouprenormalizationtensoractually
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We investigate the entanglement spectrum in HOTRG ---tensor renormalization group (RG) method combined with the higher order singular value decomposition--- for two-dimensional (2D) classical vertex models. In the off-critical region, it is explained that the entanglement spectrum associated with the RG transformation is described by `doubling' of the spectrum of a corner transfer matrix. We then demonstrate that the doubling actually occurs for the square-lattice Ising model by HOTRG calculations up to $D = 64$, where $D$ is the cut-off dimension of tensors. At the critical point, we also find that a non-trivial $D$ scaling behavior appears in the entanglement entropy. We mention about the HOTRG for the 1D quantum system as well.

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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. 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.

  2. 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.

  3. Entanglement entropy by tensor renormalization group approach

    hep-lat 2025-02 conditional novelty 6.0 of 10

    A HOTRG-based algorithm computes entanglement entropy for arbitrary subsystem sizes and recovers the central charge c=0.49997(8) for the critical Ising chain.

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