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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 3rd 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe term "tensor network", while essentially just a synonym for "string diagram", has in recent years become widely used and now fully established in quantum physics, especially in its use for discussion of _[[holographic entanglement entropy]]_. It needs a page of its own, if only to point to _[[string diagram]]_ while also listing the relevant physics references <a href="https://ncatlab.org/nlab/revision/tensor+networks/1">v1</a>, <a href="https://ncatlab.org/nlab/show/tensor+networks">current</a>

   The term “tensor network”, while essentially just a synonym for “string diagram”, has in recent years become widely used and now fully established in quantum physics, especially in its use for discussion of holographic entanglement entropy. It needs a page of its own, if only to point to string diagram while also listing the relevant physics references

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 3rd 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexmade page name singular <a href="https://ncatlab.org/nlab/revision/tensor+network/1">v1</a>, <a href="https://ncatlab.org/nlab/show/tensor+network">current</a>

   made page name singular

   v1, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 24th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's * [[Jacob Biamonte]], _Lectures on Quantum Tensor Networks_ ([arXiv:1912.10049](https://arxiv.org/abs/1912.10049)) <a href="https://ncatlab.org/nlab/revision/diff/tensor+network/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/tensor+network/8">v8</a>, <a href="https://ncatlab.org/nlab/show/tensor+network">current</a>

   added pointer to today’s

   • Jacob Biamonte, Lectures on Quantum Tensor Networks (arXiv:1912.10049)

   diff, v8, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeFeb 7th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to this recent review: * Roman Orus, _Tensor networks for complex quantum systems_, Nature Reviews Physics 1, 538-550 (2019) ([arXiv:1812.04011](https://arxiv.org/abs/1812.04011), [doi:10.1038/s42254-019-0086-7](https://doi.org/10.1038/s42254-019-0086-7)) <a href="https://ncatlab.org/nlab/revision/diff/tensor+network/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/tensor+network/14">v14</a>, <a href="https://ncatlab.org/nlab/show/tensor+network">current</a>

   added pointer to this recent review:

   • Roman Orus, Tensor networks for complex quantum systems, Nature Reviews Physics 1, 538-550 (2019) (arXiv:1812.04011, doi:10.1038/s42254-019-0086-7)

   diff, v14, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeFeb 7th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarted to add some actual content to the Idea section ([here](https://ncatlab.org/nlab/show/tensor+network#Idea)) <a href="https://ncatlab.org/nlab/revision/diff/tensor+network/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/tensor+network/15">v15</a>, <a href="https://ncatlab.org/nlab/show/tensor+network">current</a>

   started to add some actual content to the Idea section (here)

   diff, v15, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeFeb 7th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Roman Orus]], _A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States_, Annals of Physics 349 (2014) 117-158 ([arXiv:1306.2164](https://arxiv.org/abs/1306.2164)) <a href="https://ncatlab.org/nlab/revision/diff/tensor+network/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/tensor+network/16">v16</a>, <a href="https://ncatlab.org/nlab/show/tensor+network">current</a>

   added pointer to:

   • Roman Orus, A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States, Annals of Physics 349 (2014) 117-158 (arXiv:1306.2164)

   diff, v16, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeFeb 7th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded also pointer to this review: * F. Verstraete, J. I. Cirac, V. Murg, _Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems_, Adv. Phys. 57,143 (2008) ([arXiv:0907.2796](https://arxiv.org/abs/0907.2796)) <a href="https://ncatlab.org/nlab/revision/diff/tensor+network/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/tensor+network/16">v16</a>, <a href="https://ncatlab.org/nlab/show/tensor+network">current</a>

   added also pointer to this review:

   • F. Verstraete, J. I. Cirac, V. Murg, Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems, Adv. Phys. 57,143 (2008) (arXiv:0907.2796)

   diff, v16, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeFeb 7th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexand this one: * J. Eisert, _Entanglement and tensor network states_, Modeling and Simulation 3, 520 (2013) ([arXiv:1308.3318](https://arxiv.org/abs/1308.3318)) <a href="https://ncatlab.org/nlab/revision/diff/tensor+network/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/tensor+network/16">v16</a>, <a href="https://ncatlab.org/nlab/show/tensor+network">current</a>

   and this one:

   • J. Eisert, Entanglement and tensor network states, Modeling and Simulation 3, 520 (2013) (arXiv:1308.3318)

   diff, v16, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeFeb 8th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItex*Question:* Does any (other) author discuss tensor network states specifically for trivalent networks with a _Lie bracket_ tensor (Lie structure constants) on each vertex?

   Question:

   Does any (other) author discuss tensor network states specifically for trivalent networks with a Lie bracket tensor (Lie structure constants) on each vertex?

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeFeb 8th 2020
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded further graphics to the Idea-section <a href="https://ncatlab.org/nlab/revision/diff/tensor+network/22">diff</a>, <a href="https://ncatlab.org/nlab/revision/tensor+network/22">v22</a>, <a href="https://ncatlab.org/nlab/show/tensor+network">current</a>

    added further graphics to the Idea-section

    diff, v22, current

11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeApr 10th 2020
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to today's * Alexander Jahn, Zoltán Zimborás, [[Jens Eisert]], _Tensor network models of AdS/qCFT_ ([arXiv:2004.04173](https://arxiv.org/abs/2004.04173)) <a href="https://ncatlab.org/nlab/revision/diff/tensor+network/33">diff</a>, <a href="https://ncatlab.org/nlab/revision/tensor+network/33">v33</a>, <a href="https://ncatlab.org/nlab/show/tensor+network">current</a>

    added pointer to today’s

    • Alexander Jahn, Zoltán Zimborás, Jens Eisert, Tensor network models of AdS/qCFT (arXiv:2004.04173)

    diff, v33, current

12. • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeNov 30th 2021
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to this recent review: * Kouichi Okunishi, Tomotoshi Nishino, Hiroshi Ueda, *Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement* ([arXiv:2111.12223](https://arxiv.org/abs/2111.12223)) <a href="https://ncatlab.org/nlab/revision/diff/tensor+network/44">diff</a>, <a href="https://ncatlab.org/nlab/revision/tensor+network/44">v44</a>, <a href="https://ncatlab.org/nlab/show/tensor+network">current</a>

    added pointer to this recent review:

    • Kouichi Okunishi, Tomotoshi Nishino, Hiroshi Ueda, Developments in the Tensor Network – from Statistical Mechanics to Quantum Entanglement (arXiv:2111.12223)

    diff, v44, current