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Remote detectability from entanglement bootstrap I: Kirby's torus trick
by Bowen Shi, Jin-Long Huang, John McGreevy
Submission summary
| Authors (as registered SciPost users): | John McGreevy · Bowen Shi |
| Submission information | |
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| Preprint Link: | scipost_202306_00003v2 (pdf) |
| Date submitted: | 2024-10-17 00:58 |
| Submitted by: | Shi, Bowen |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Remote detectability is often taken as a physical assumption in the study of topologically ordered systems, and it is a central axiom of mathematical frameworks of topological quantum field theories. We show under the entanglement bootstrap approach that remote detectability is a necessary property; that is, we derive it as a theorem. Starting from a single wave function on a topologically-trivial region satisfying the entanglement bootstrap axioms, we can construct states on closed manifolds. The crucial technique is to immerse the punctured manifold into the topologically trivial region and then heal the puncture. This is analogous to Kirby's torus trick. We then analyze a special class of such manifolds, which we call pairing manifolds. For each pairing manifold, which pairs two classes of excitations, we identify an analog of the topological $S$-matrix. This pairing matrix is unitary, which implies remote detectability between two classes of excitations. These matrices are in general not associated with the mapping class group of the manifold. As a by-product, we can count excitation types (e.g., graph excitations in 3+1d). The pairing phenomenon occurs in many physical contexts, including systems in different dimensions, with or without gapped boundaries. We provide a variety of examples to illustrate its scope.
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
Author comments upon resubmission
List of changes
1. We added a footnote in the introduction (on page 5). We mentioned explicitly that part of the data carried by the large ball (associated with the reference state) is a cell complex. The topology can thus be defined using the cell complex.
2. We edited footnotes 8, 9, and 12 to make the meaning more clear. In particular, in footnote 9, we commented that continuum topology is not needed for our purpose. The purpose of the ``extra thickness'' is explained in footnote 12, and we explained why this is well under control. This should remove the confusion that worries the referee.
3. We added a Remark on page 40, after the statement of the completion trick. This remark addresses the definition of topology from the cell decomposition.
Current status:
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Report
The updated manuscript adequately clarifies the relationship of the setup of entanglement bootstrap to continuum topology. I believe that the discussion as presented is logically consistent, and includes necessary caveats and disclaimers wherever certain reasonable assumptions are made without rigorous proof.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)