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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): | Arnab Sen · Krishnendu Sengupta |
| Submission information | |
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| Preprint Link: | scipost_202411_00003v1 (pdf) |
| Date submitted: | 2024-11-02 03:49 |
| 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.
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List of changes
We have now addressed the comments of the first referee by adding a paragraph in the discussion section citing
references on DMRG and QMC and discussing their relevance to the present work.
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In this paper, the authors study a constrained boson model with a subsystem symmetry on a "diamond chain" lattice. While a quantum phase transition of Ising universality class is expected, the authors claim that the actual transition belongs to the Ashkin-Teller universality class.
The model and various consequences of the subsystem symmetry is certainly interesting. However, I feel that the nature of the ground-state phase diagram and the quantum phase transition is not clarified enough. The main claim that the transition belongs to the Ashkin-Teller universality class is also not sufficiently justified in my view.
First, in the $\lambda \gg w$ region, the authors find "gapless" phase with a spontaneously broken $\mathbb{Z}_2$ symmetry. I see he authors' argument why the system is "gapless" (in a certain sense) in the limit $\lambda \gg w$. However, this seems to be attributed to a motion of a single defect, and does not seem to lead to gapless excitations with non-vanishing density of states in the thermodynamic limit. In other words, is the "gapless" phase described by a CFT? I suspect it corresponds to $c=0$ (if you study the low-temperature limit of the specific heat, for example). If the "gapless" nature discussed by the authors just comes from the motion of a single defect, it sounds more like an artifact and does not constrain the bulk behavior in the thermodynamic limit. In any case, the authors should clarify what "gapless" means for this phase.
The claim that the phase transition belongs to the Ashkin-Teller universality class also looks weak to me. Apparently it is based on the numerical estimate of the central charge --- it looks significantly larger than the Ising value of 1/2. However, it does not also show that the central charge is the Ashkin-Teller value of 1. As the authors claim, maybe it is consistent with the hypothesis that the universality class is Ashkin-Teller. But I do not feel it is strong enough to be regarded as an evidence. Just as a possiblity, the presence of the moving defect might be "contaminating" the numerical central charge data, and the actual central charge could be Ising. I am not claiming this is true, but from what I find in the paper I cannot rule out such a possiblity.
Ashkin-Teller universality class is not just characterized by the central charge 1. The operator content is also well-understood. In particular, there must be the twist (or spin) operators with the conformal dimension (1/16,1/16) in the spectrum independently of the compactification radius ("Luttinger parameter"). There are also vertex operators whose conformal dimensions depend on the radius. I suggest the authors to study the operator content from the spectrum, in addition to the central charge.
Finally, the phase diagram of the Ashkin-Teller model has been studied in many papers, and we can understand the phase diagram in terms of the perturbations to the Ashkin-Teller CFT. In order to establish the claim, I think the authors should make such an analysis for the present model.
Some minor (non-essential) comments:
- I think the authors' lattice is sometimes called as "diamond chain lattice" in quantum spin systems community. Perhaps they can mention this.
- The original form of Eq. (11) (although not exactly Eq. (11) for open boundary conditions) was derived by Holzhey, Larsen, and Wilczek in Nucl.Phys. B424 443 (1994). Perhaps it is fair to cite it along with Calabrese-Cardy.
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Ask for major revision
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The authors have included a further discussion on potential extension to this subject with other numerical methods. Although I still think claiming the critical point is AT like requires stronger evidence, this paper, however, does propose a new direction to study systems with constraints. With that, I recommend this paper to be published in SciPost.
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Publish (easily meets expectations and criteria for this Journal; among top 50%)