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Entanglementenabled symmetrybreaking orders
by ChengJu Lin, Liujun Zou
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Submission summary
Authors (as registered SciPost users):  ChengJu Lin · Liujun Zou 
Submission information  

Preprint Link:  scipost_202305_00001v2 (pdf) 
Date submitted:  20231030 15:54 
Submitted by:  Lin, ChengJu 
Submitted to:  SciPost Physics Core 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
A spontaneous symmetrybreaking order is conventionally described by a tensorproduct wavefunction of some fewbody clusters; some standard examples include the simplest ferromagnets and valence bond solids. We discuss a type of symmetrybreaking orders, dubbed entanglementenabled symmetrybreaking orders, which cannot be realized by any such tensorproduct state. Given a symmetrybreaking pattern, we propose a criterion to diagnose if the symmetrybreaking order is entanglementenabled, by examining the compatibility between the symmetries and the tensorproduct description. For concreteness, we present an infinite family of exactly solvable gapped models on onedimensional lattices with nearestneighbor interactions, whose ground states exhibit entanglementenabled symmetrybreaking orders from a discrete symmetrybreaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglementenabled symmetry breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetryprotected 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 entanglementenabled symmetrybreaking 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
Report #2 by Anonymous (Referee 4) on 202427 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202305_00001v2, delivered 20240207, doi: 10.21468/SciPost.Report.8512
Report
This paper tries to propose the idea of "Entanglementenabled symmetrybreaking 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 LiebSchultzMattis 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 halfinteger 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 wavefunction. 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: ChengJu Lin on 20240218 [id 4315]
(in reply to Report 2 on 20240207)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 shortrange 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.