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Background independent tensor networks
by Chris Akers, Annie Y. Wei
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Submission summary
| Authors (as registered SciPost users): | Christopher Akers |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2402.05910v3 (pdf) |
| Date accepted: | 2024-09-10 |
| Date submitted: | 2024-07-26 19:21 |
| Submitted by: | Akers, Christopher |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Conventional holographic tensor networks can be described as toy holographic maps constructed from many small linear maps acting in a spatially local way, all connected together with ``background entanglement'', i.e. links of a fixed state, often the maximally entangled state. However, these constructions fall short of modeling real holographic maps. One reason is that their ``areas'' are trivial, taking the same value for all states, unlike in gravity where the geometry is dynamical. Recently, new constructions have ameliorated this issue by adding degrees of freedom that ``live on the links''. This makes areas non-trivial, equal to the background entanglement piece plus a new positive piece that depends on the state of the link degrees of freedom. Nevertheless, this still has the downside that there is background entanglement, and hence it only models relatively limited code subspaces in which every area has a definite minimum value given by the background entanglement. In this note, we simply point out that a version of these constructions goes one step further: they can be background independent, with no background entanglement in the holographic map. This is advantageous because it allows tensor networks to model holographic maps for larger code subspaces. In addition to pointing this out, we address some subtleties involved in making it work and point out a nice connection it offers to recent discussions of random CFT data.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
We have made a number of changes listed in response to the referee's detailed suggestions.
Published as SciPost Phys. 17, 090 (2024)
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2024-9-2 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2402.05910v3, delivered 2024-09-02, doi: 10.21468/SciPost.Report.9693
Strengths
The paper is clearly written. It has a nice idea of applying properties of lattice gauge theory in the construction of holographic network to make it more graph independent.
Weaknesses
The construction is still at a very primitive state. The space of possible tensors remain extremely large and there are very few guiding principles (which is a general issue confronted by holographic tensor networks) to make progress towards making the bulk geometry concrete.
As it stands, it remains hard to include dynamics which is another long standing issue in tensor network constructions.
There should be in the future more work done in restricting the group G and perhaps restricting or replacing the random tensors.
Report
The paper makes use of graph independence in constructing gauge invariant lattice gauge theory wave-function to construct graph independent holographic tensor network. The construction is reasonable, and it is perhaps as concrete as one could achieve at present from considerations pertaining to entanglement pattern and some level of graph independence.
The authors have also addressed other comments of referee 1.
I would recommend the paper for publication in sci-post.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)