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Entanglement-enabled symmetry-breaking orders
by Cheng-Ju Lin, Liujun Zou
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Submission summary
| Authors (as registered SciPost users): | Cheng-Ju Lin · Liujun Zou |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202305_00001v2 (pdf) |
| Date submitted: | 2023-10-30 15:54 |
| Submitted by: | Lin, Cheng-Ju |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
A spontaneous symmetry-breaking order is conventionally described by a tensor-product wavefunction of some few-body clusters; some standard examples include the simplest ferromagnets and valence bond solids. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any such tensor-product state. Given a symmetry-breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry-breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry- breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.
List of changes
Along with various minor changes, here is a summary of the major changes.
1. We have highlighted the defintion of EESBO.
2. We have added a sentence in Sec. 2 to emphasize that we are considering ground states of local Hamiltonians.
3. We have added a sentence at the end of Sec. 2 to emphasize the difference between entanglement-enabled symmetry-breaking orders and the usual phenomenon of coexistence of spontaneous symmetry breaking and nontrivial topological phases.
4. We have added a sentence in Sec. 5 to provide further insights to the example there.
Current status:
Reports on this Submission
Anonymous Report 2 on 2024-2-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202305_00001v2, delivered 2024-02-07, doi: 10.21468/SciPost.Report.8512
Report
This paper tries to propose the idea of "Entanglement-enabled symmetry-breaking orders" with several examples. The first example is the same as that discussed in SciPostPhys.11.2.024. In that paper, the fact that there is no simple product state satisfying all the symmetries is presented as an example of the "generalized Lieb-Schultz-Mattis theorem", while in this paper, the authors tried to argue that this example is not covered by the LSM theorem. Of course, one may say that this is a matter of definition, but this example has a lot of similarities with the original LSM example. I tend to agree with the author of SciPostPhys.11.2.024 and consider this example as a generalized LSM. The second example is interesting where the authors pointed out that any pure state of a spin 1/2 has a residue U(1) symmetry, therefore no product state of spin 1/2's can break the SO(3) symmetry down to Z2. This is an interesting observation, although this is a fragile phenomenon in the sense that if other half-integer spin representations are allowed, such an obstruction no longer exists. It is therefore important to not only enforce the symmetry but also enforce the symmetry representation on each lattice site. The last example has been discussed in Phys. Rev. B 94, 064432 as a "featureless quantum insulator" without a tensor product wave-function. So this example is again known.
This paper grouped several examples together, some with a higher level of innovation than others. On the other hand, the paper did not present a unified mechanism that explains all these examples and predicts new ones. The examples are kind of ad hoc. Because of this, I agree with the referees that the level of innovation in this paper is low. Some of the examples are interesting and the paper may be worth publishing because of that.
Author: Cheng-Ju Lin on 2024-02-18 [id 4315]
(in reply to Report 2 on 2024-02-07)We thank Referee for the comments in the report. We have added the last paragraph in Sec. 4, clarifying the difference between our construction and the construction in Ref.[18] (Jiang et. al.). In particular, our construction has spontaneous symmetry breaking while Ref. [18] does not. Moreover, our diagnostic of EESBO does not use the property of short-range entangled states having nontrivial edge modes.
We thank Referee's comment again so that we can clarify the difference between our construction and the construction in Ref.[18] in the main text.