SciPost Submission Page
Emergent Ashkin-Teller criticality in a constrained boson model
by Anirudha Menon, Anwesha Chattopadhyay, K. Sengupta, Arnab Sen
Submission summary
| Authors (as registered SciPost users): | Anwesha Chattopadhyay · Arnab Sen · Krishnendu Sengupta |
| Submission information | |
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| Preprint Link: | scipost_202411_00003v2 (pdf) |
| Date submitted: | 2025-01-16 12:51 |
| Submitted by: | Sengupta, Krishnendu |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We show, via explicit computation on a constrained bosonic model, that the presence of subsystem symmetries can lead to a quantum phase transition (QPT) where the critical point exhibits an emergent enhanced symmetry. Such a transition separates a unique gapped ground state from a gapless one; the latter phase exhibits a broken $Z_2$ symmetry which we tie to the presence of the subsystem symmetries in the model. The intermediate critical point separating these phases exhibits an additional emergent $Z_2$ symmetry which we identify; this emergence leads to a critical theory in the Ashkin-Teller, instead of the expected Ising, universality class. We show that the transitions of the model reproduces the Askhin-Teller critical line with variable correlation length exponent $\nu$ but constant central charge $c$. We verify this scenario via explicit exact-diagonalization computations, provide an effective Landau-Ginzburg theory for such a transition, and discuss the connection of our model to the PXP model describing Rydberg atom arrays.
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) Added comments in Sec 2 regarding flat bands in diamond lattice in response to suggestions by the editor. Also added Ref 34.
2) Added comment in Sec 3 regarding quadratic energy dispersion of the model in the gapless phase in response to comment by Ref 2.
3) Added comment on diamond chain lattice in Sec 2 in response to suggestion by Ref 2.
4) Added ref 25 in response to comment by Ref 2.
5) Added a comment in the discussion section of the paper clarifying the notion of subsystem symmetry in response to comment by Ref 3.
6) Added Refs 38 and 39 in response to comment on Schrieffer-Wolfe transformation by Ref 3.
7) Added a discussion on the sign of the parameter $\alpha$ in Sec 2 in response to comment by Ref 3. Al;so added Refs 38 and 39 in this context.
Current status:
Reports on this Submission
Report
In my opinion, the authors make a reasonable case that their numerical results are consistent with the Ashkin-Teller universality class. However, I agree with Report #1 by Anonymous (Referee 2) on 2025-2-21 that the comment at the end of section 5 is very strange. My understanding is that certain boundary conditions may project out the sector of the ground state from the Hilbert space. Then one sees an effective central charge as defined, e.g., in Ref. [45]. However, this does not mean that the true central charge does indeed change. After all, a change of boundary conditions should not change the bulk physics, at least not in a system with short-range interactions. If the emergent $\mathbb{Z}_2$ symmetry is supposed to hinge on these boundary conditions, this is actually worrisome. In any case, this point needs to be clarified before the manuscript can be published.
Beyond this, I regret to say that I do not have the impression of a finished manuscript even if it already went through several rounds of revision, specifically:
A) The Landau-Ginzburg section 4.2 is very short and its role did not become completely clear to me. Also, I do not think that a Landau-Ginzburg theory will yield the correct critical exponents, but the universality class of the transition is the main focus of the present work.
B) The role of section 3.1 ("Numerical results") is not quite clear either. In particular, this comprises two references to entanglement entropy on less than one page, but no data is shown. I think that the authors should either show the data (if they consider it important) or remove these remarks.
C) Appendix A makes the impression of an excuse to cite Refs. [50,51] by the group itself. By contrast, references for the well-known definition of entanglement entropy are missing. I recommend to cut this down to the essence, move the remainder into an appropriate place of the main text, and add references for the definition of the entanglement entropy $S_E$.
There are further issues of a more typographic nature that I list below among "Requested changes".
Requested changes
Major points:
1) Clarify the discussion of the central charge $c$ in relation to boundary conditions at the end of section 5.
2) Consider moving the Landau-Ginzburg section 4.2 to an appendix, add remarks on its role, and remove it from the abstract (after all, this cannot be a main point of this work).
3) Clarify the role of section 3.1 ("Numerical results"). Furthermore, either show the results for the entanglement entropy or remove the related remarks from section 3.1.
4) Shorten appendix A, move the result into the main text, and add references for the definition of the entanglement entropy $S_E$.
Minor points (typographical errors etc.):
5) Third paragraph of section 1: "disordered Ising system" $\to$ "disordered Ising systems".
6) Third line of section 2: "have been discussed" $\to$ "has been reviewed". After all, Ref. [34] is a review, the original publications are older than that.
7) Fig. 1 appears to be a low-quality and thus fuzzy image. Ideally, it would be converted to a vector graphics; at the very least, resolution should be increased.
8) Eq. (1) should terminate with a full stop (".").
9) First line of section 3: "two limit" $\to$ "two limits".
10) Eq. (7) should terminate with a full stop ("."), not a comma (",").
11) Figs. 5, 7, 6 seem to be cited in this order and thus should be reordered according to their appearance in the text.
12) Fourth line of section 4: In my opinion "It is well known" needs nevertheless to be substantiated by references.
13) Third line of caption of Fig. 1: I think an article "the" is missing on front of "Ising model".
14) I believe that Fig. 7(c) corresponds to $\alpha=1$, but that should be stated in the figure caption.
15) Eq. (15) should terminate with a full stop (".").
16) Last line of page 13: "One of the source" $\to$ "One of the sources".
17) First paragraph on page 14: "loan" $\to$ "lone"?
18) First line of second paragraph of on page 14: "finite-sized analysis" $\to$ "finite-size analysis".
19) Second line of page 15: insert "standard" before "density-matrix-renormalization group". After all, this is followed be a statement that there are variants that do the job.
20) Second line of second paragraph of on page 15: "a ultracold" $\to$ "an ultracold".
21) Line below Eq. (21): "$rho$" $\to$ "$\rho$".
22) Fix issues with the bibliography:
[7,14,16-18,20,24,33,38-40,42,45,48-51] Lower-casing of names in titles ("Ashkin", "Elitzur", "Floquet", "Ising", "Mott", "Rydberg", "Teller", "Wolff").
[22] "q" $\to$ "Q" and "u(1)" $\to$ "U(1)".
[24] "n=2" $\to$ "N=2".
[47] Break the title such that at least it does not spill beyond the boundary of the page.
Recommendation
Ask for major revision
Report
I appreciate the efforts made by the authors to improve the paper, but I am still not convinced that the claim of the Ashkin-Teller universality class is supported well enough. I believe that the operator content can be studied numerically in spite of the unclear relation to the microscopic operators mentioned by the author. I am also confused with the comment "a change in boundary condition may change $c$ (central charge)" at the end of Section 5. I did check Ref. [45], and if you *define* the "effective central charge" as in Ref. [45] it would be true, but perhaps it is rather a misnomer. As a general principle, the boundary conditions should not alter the bulk universality class which is characterized by the central charge. If the author somehow implies that Ref. [45] is related to the claim of the (bulk) Ashkin-Teller universality class, I am afraid that they are mistaken.
It is also not clear to me how the discussion in Sec. 4.2 is related to the specific model in question.
On the other hand, as I mentioned, this paper does contain some interesting observations.
I would suggest two options:
1) Consult/collaborate with someone with a strong background of CFT to perform a more thorough comparison with CFT.
2) Revise the paper to objectively describe theoretically established statements and numerical observations. The authors may speculate/conjecture the Ashkin-Teller universality class in the Discussion section, but I think it better to remove the Ashkin-Teller from the title etc.
Recommendation
Ask for major revision