SciPost Submission Page
$\mathbb{Z}_4$ transitions in quantum loop models on a zig-zag ladder
by Bowy Miquelli La Rivière, Natalia Chepiga
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Natalia Chepiga · Bowy La Riviere |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2406.20093v1 (pdf) |
| Date submitted: | 2024-07-04 16:29 |
| Submitted by: | La Riviere, Bowy |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
We study the nature of quantum phase transitions out of $\mathbb{Z}_4$ ordered phases in quantum loop models on a zig-zag ladder. We report very rich critical behaviour that includes a pair of Ising transitions, a multi-critical Ashkin-Teller point and a remarkably extended interval of a chiral transition. Although plaquette states turn out to be essential to realize chiral transitions, we demonstrate that critical regimes can be manipulated by deforming the model as to increase the presence of leg-dimerized states. This can be done to the point where the chiral transition turns into first order, we argue that this is associated with the emergence of a critical end point.
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
Current status:
Reports on this Submission
Strengths
1. detailed and rather thorough study of phase transitions in an effective loop model, which describes the singlet sector of S=1 frustrated chains.
2. impressively large system sizes.
3. rich phase diagram reported, with rather strong evidence regarding the nature of the transitions presented.
Weaknesses
1 . While the finite size effects are shown in some plots, the bond dimension dependence is not presented to the readers.
2. The manuscript text has omissions and the introduction could be made a bit more accessible.
3. While realisation of some the physics of the loop model in experiments is alluded to, it is not highlighted
In my opinion how difficult it will be to measure the nature of the phase transitions in experiments. Can the
authors comment on how realistic it is to measure the critical exponents in Rydberg systems or condensed matter systems ?
Report
This manuscript deals with the quantum loop model description which one of the authors has previously introduced and uses this subspace to analyse a number of quantum phase transitions rather accurately. The methodology is based on dermining the correlation length xi, as well as the oscillation wave vector and its behaviour upon approaching the transition. Based on this information the exponent \nu other aspects of the transitions are inferred. However the dynamical critical exponent is not measured as such.
I think this is a paper of high scientific rigour and should be published in SciPost Physics once the suggested changes have been considered.
Requested changes
1. The notion of loop models is restricted to the authors use in this paper and their previous own work. However loop models have a broader audience, for example as cousins of quantum dimer models. There for example the quantum loop models do not allow for two loop segments to occupy the same link. Please expand the introduction of loop models and clarify the differences with other quantum loop models in quantum magnetism (e.g. square ice ground state manifold)
2. The comment on the maximum bond dimension needs clarification. I am aware of SU(N) models with effective bond dimensions ~10^6, while I would be curious to learn more what allows the present authors to reach 10'000 bond dimension, is this simply brute force, or is there some fragmentation of the total bond dimension into smaller subsection because of the nature of the quantum loop Hilbert space ?
3. Expanding the introduction: As one example I feel that the normal phase of the S=1 chain and its relation to the present problem and its location in the phase diagram would be interesting to know for people who have not yet read the authors previous papers on the subject.
Recommendation
Publish (meets expectations and criteria for this Journal)
Strengths
1 - high quality, reliable numerics
2 - provides a novel link between different research areas (frustrated spin chains, quantum loop models, Rydberg atoms)
3 - provides a novel example of a chiral Z_4 transition
Weaknesses
1 - the toy model studied has limited relevance
Report
The paper presents a thorough study of quantum phase transitions in a toy quantum dimer model on a zigzag ladder, inspired by models of frustrated spin-1 chains. It is shown that in an extended parameter range, there is transition between the Z_4 leg-dimerized phase and the "disordered" NNN-Haldane phase, which belongs to the Huse-Fischer chiral universality class. By tuning the model parameters, this transition can be suppressed into 1st order.
The results provide interesting links between different research areas (frustrated spin chains, quantum dimer models, Rydberg atoms) and thus deserve to be published in SciPost.
As a minor shortcoming, one can mention that the realization of the proposed quantum dimer model with the Rydberg atoms on a circular ladder is rather complicated: in addiition to the NNN blockade required for the "inner" circle/leg vs only NN blockade for the outer leg, the constraints require the NN blockade between the inner and outer legs as well; to my opinion, this is not very realistic.
Another minor comment is that it might be confusing that the NNN-Haldane phase is called "disordered" throughout the text, as in possesses a nonlocal order (see Ref.33). It should be remarked that the dimer model considered is constructed in a way that explicitly disfavors the "usual" Haldane phase (which would as well be "disordered" for the purpose of this paper).
Recommendation
Publish (meets expectations and criteria for this Journal)