SciPost Submission Page
Entanglementenabled symmetrybreaking orders
by ChengJu Lin, Liujun Zou
This is not the latest submitted version.
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users):  ChengJu Lin · Liujun Zou 
Submission information  

Preprint Link:  scipost_202305_00001v1 (pdf) 
Date submitted:  20230501 16:58 
Submitted by:  Lin, ChengJu 
Submitted to:  SciPost Physics 
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 \textit{cannot} be realized by any such tensorproduct state. Given a symmetry breaking 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 symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglementenabled symmetrybreaking 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.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 202379 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202305_00001v1, delivered 20230709, doi: 10.21468/SciPost.Report.7478
Strengths
 Clear and simple
 Interesting idea
Weaknesses
 Not application found
 Missing a classification
Report
The paper is interesting but I think SciPost core fits more for the publication.
The definition of EESBO should be highlight. Maybe talk about the lack of a basis that enable to write the ground states in a product form. Maybe also put an example of not EESBO and long range like the GHZ state from the 2fold degenerate ground state of the Ising model.
I have some questions about the mechanism of EESBO. The paper considers SPT phases that are not conventional but I think this is not required. Let us consider an ordinary G0= Z2x(ZnxZn) and go to G=ZnxZn; breaking the Z2 symmetry that could be internal and not a lattice symmetry. With the regular SPT classification the 2 ground states could be in n different SPT phases, n1 of them nontrivial and therefore not able to be written as a product state because of the entanglement given by the projective representation. Why are not those EESBO? If they are, why are they not considered?
I guess that the family of states can be generalized to break T to T^m and have mdegenerate ground states.
Most readers won't be familiar with these unconventional SPT phases. I am familiar with the standard understanding of projective representations at the bonds giving rise to standard SPT phases (also with MPSs) and the RGFP cartoon picture of entangled pairs between sites. Is there an easy characterization or cartoon picture of these unconventional SPT phases? I think it would help a lot if the paper describes them.
Requested changes
See report. Clarify definition and SPT cases
Report #1 by Anonymous (Referee 1) on 202368 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202305_00001v1, delivered 20230608, doi: 10.21468/SciPost.Report.7324
Strengths
Interesting idea about classifying symmetry breaking.
Weaknesses
Not written very clearly.
Report
The manuscript "EntanglementEnabled SymmetryBreaking Order" seems
interesting to me. As I understand it, the strategy is to first
specify a symmetry of a full hilbert space (or define a symmetry),
then consider how this symmetry might break. If the broken symmetry
can never be a local product state, then it is declared to be a EESBO.
What is not clear to me is whether this manner of classifying broken
symmetries is going to turn out to be useful or not.
There appears to be no requirement that the state in question is
gapped, or even that it is the ground state of any Hamiltonian. This
work is simply making statements about wavefunctions with some
symmetry that live within a Hilbert space with some symmetry. If this
is so, is this a feature or a bug? Does it suggest that the
classification may end up classifying many things that are not phases
of matter in any sense?
Overall I nonetheless think the paper is interesting and should be
published. I'm not sure there will be overwhelming interest, so I
suggest SciPost core rather than the flagship SciPost.
To give some suggestions, I do have to say that the paper was
extremely hard for me to read. While there is a small community who
is very familiar with these types of arguments, I fear that most even
welleducated condensed matter theorists will find much of the
arguments to be very obtuse.
The examples seem needlessly difficult to think about. For example,
section 5.2 seems the simplest example (at least to me) because one
can take a limit fo a=b=c=1 and then the wavefunction is supereasy to
describe and you can just look at it and see what is going on. Trying
to do it in generality makes it completely impossible to understand.
Similarly, the entire example in section 4 is insanely arcane.
Even in section 5, the authors insist on doing a 3d example,
presumably to evade MerminWagner. But there is no point in this.
Since we didn't ever specify a Hamiltonian, why not just assume it is
a longranged Hamiltonian, so that MerminWagner does not apply.
(Indeed, the Hamiltonian doesn't matter anyway!) Then you can just
talk about spin chains (Am I wrong about this?).
I would recommend that before publication, the authors try very hard
to simplify much the discussion, clarify the writing, and put all the
simple examples up front. Yes, I know this is hard to do, but it
really will pay off in the end. If you write a paper that only a tiny
fraction of the community can bother to understand, then it won't have
much impact.
Also note, the paragraph where the EESBO is defined in section 2 gives the
definition almost as a side comment. One can read the paragraph and
not even realize that there has just been a definition made. Please
state it clearly and precisely, not so casually, so people know what
you are talking about! And flag it clearly
"DEFINITION: GIven X,Y, Z, we say that a wavefunction is EESBO if P,
Q, R"
Requested changes
See report. Please simplify examples and write more clearly for a bigger audience.
Author: ChengJu Lin on 20231030 [id 4079]
(in reply to Report 1 on 20230608)
We thank Referee for the valuable report. We have prepared the response in the following PDF file.
Sincerely,
ChengJu Lin and Liujun Zou
Author: ChengJu Lin on 20231030 [id 4078]
(in reply to Report 2 on 20230709)We thank Referee for the valuable report. We have prepared the response in the following PDF file.
Sincerely,
ChengJu Lin and Liujun Zou
Attachment:
Response.pdf