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Cited by 9Quantum many-body systemsBlack Holes and Theoretical PhysicsAlgebraic structures and combinatorial models

Tensor chain and constraints in tensor networks

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Ling, Yi, Liu, Yuxuan, Xian, Zhuo-Yu, Xiao, Yikang·2019·Journal of High Energy Physics
DOI 10.1007/jhep06(2019)032
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Abstract

We develop our recent work on quantum error correction (QEC) and entanglement spectrum (ES) in tensor networks (arXiv:1806.05007). We propose a general framework for planar tensor network state with tensor constraints as a model for AdS 3/CFT 2 correspondence, which could be viewed as a generalization of hyperinvariant tensor networks recently proposed by Evenbly. We elaborate our proposal on tensor chains in a tensor network by tiling H 2 space and provide a diagrammatical description for general multi-tensor constraints in terms of tensor chains, which forms a generalized greedy algorithm. The behavior of tensor chains under the action of greedy algorithm is investigated in detail. In particular, for a given set of tensor constraints, a critically protected (CP) tensor chain can be figured out and evaluated by its average reduced interior angle. We classify tensor networks according to their ability of QEC and the flatness of ES. The corresponding geometric description of critical protection over the hyperbolic space is also given.

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Crossref · 10.1007/jhep06(2019)032

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43 of 43 references verified0 citation errors · 0 not checkable

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  • Three-valent intertwiners, as well as two-valent vertices with linear independent tangent vectors, are eigenstates of S_v as shown in [45].

    “Three-valent intertwiners, as well as two-valent vertices with linear independent tangent vectors are eigenstates of S v as shown in [45].”

    From Hyperinvariant spin network states — an AdS/CFT model from first principles (2026) · cites this paper as [45]

  • Two-valent vertices with spin j and non-parallel tangent vectors are also eigenstates and contribute with eigenvalue j(j+1) as shown in Ref. [45].

    “Furthermore, two-valent vertices with spin j and non-parallel tangent vectors are also eigenstates and contribute with an eigenvalue j(j + 1) as shown in Ref. [45].”

    From Hyperinvariant spin network states — an AdS/CFT model from first principles (2026) · cites this paper as [45]

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Authors
Ling, Y., Liu, Y., Xian, Z.-Y., & Xiao, Y.
Affiliations
Chinese Academy of Sciences (CN)
Corresponding author
Xiao, Yikang
ORCID
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2019-06
Volume
2019
Issue
6
ISSN
1029-8479 (ISSN-L)
DOI
10.1007/jhep06(2019)032
OpenAlex
W2949379296
Cited by
8
References
43
Citations by year
2024: 1 · 2023: 1 · 2022: 3 · 2020: 1 · 2019: 2
FWCI
0.66
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of High Energy Physics (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University)
Funders
  • National Natural Science Foundation of China (11847229, 11875053, 11575195)
  • China Postdoctoral Science Foundation (BX20180318)
  • National Postdoctoral Program for Innovative Talents (BX20180318)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
Keywords
tensor networks, quantum error correction, entanglement spectrum, AdS3/CFT2 correspondence, hyperbolic space, greedy algorithm

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