SciPost Submission Page
Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
by Sergio Cerezo-Roquebrún, Simon Hands, Alejandro Bermudez
Submission summary
| Authors (as registered SciPost users): | Sergio Cerezo-Roquebrún |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2506.18675v2 (pdf) |
| Date submitted: | Oct. 31, 2025, 12:03 p.m. |
| Submitted by: | Sergio Cerezo-Roquebrún |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model using matrix product state (MPS) simulations. At zero temperature and along the symmetry line of the phase diagram, we find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation. For weak interactions, doping the symmetry-protected topological (SPT) phase of the GNW model leads to localized charges or holes at periodic arrangements of immobile topological defects separating the fragmented subchains: a topological crystal. Increasing the interactions, we observe a transition into a parity-broken phase with a pseudoscalar condensate displaying a modulated periodic pattern. This soliton lattice is a sequence of topological charges corresponding to anti-kinks, which also bind the doped fermions at their respective centers. Out of this symmetry line, we show that quasi-spiral profiles appear with a characteristic wavevector set by the density $k = 2{\pi}{\rho}$, providing non-perturbative evidence for chiral spirals beyond the large-N limit. These results demonstrate that various exotic inhomogeneous phases can arise in lattice field theories, and motivate the use of quantum simulators to confirm such QCD-inspired phenomena in future experiments.
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
Report
I recommend this work for publication in SciPost physics, with the following comments:
-It would be good to add "in 1+1D" after "single-flavor Gross-Neveu-Wilson (GNW) model" in the abstract for clarity (unless GNW already implies 1+1D, in which it could be used as an adjective for those unfamiliar with the model)
-Is the "factorization" of the chains claimed the same as fragmentation, or is it a byproduct of the fragmentation? Figures 11 and 13 discuss this "factorization" as well as "fragmentation" in similar contexts, with the chains having the same number of repeats as n_f. I think it would be good to clarify the connection between the two more. Is fragmentation being defined in a standard way here? If the fragmentation is scaling with factorization, then it seems to scale with \mu rather than the size of the Hilbert space. I found the switch between the two phrasings to be confusing.
-What can be done for this model in 2+1D and higher? I recognize that tensor networks scale exponentially with the volume, but with the fragmentation effects, perhaps certain aspects could still be studied? In IV. B. 3. there is a discussion for how energies were calculated (and high degeneracies in the ground state predicted) using various combinations of two MPS segments pasted together. Perhaps for high degrees of factorizations in higher dimensions some analysis is possible? It would be useful to comment a bit more on possibilities (or limitations) of the current approach to higher dimensions of Gross-Neveu models.
I also have these minor comments:
-There's a I.A. but not a I.B. in the introduction--it should be organized so that this isn't the case.
-Figures 7 and 17 would benefit from legends. in Figure 7 it's not so clear in black-and-white which label corresponds to which group of data, and in Figure 17 there aren't labels on the data, only a reference to color in the caption. The other figures all either have legends or clearly placed labels in addition to the caption references.
Requested changes
- Connect "factorization" and "fragmentation" more clearly in the manuscript, clarify the type of fragmentation (how it scales).
- Clarify more how this method can (or cannot) be extended to higher dimensional Gross Neveu models.
- Fix the I.A. but no I.B. organization issue in the introduction. Other changes listed as bullet points in the report are at the level of suggestions.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
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This article is written in a clear, pedagogical, and concise style. In particular, it contains a detailed introduction that explains clearly the context and all the motivations behind this study.
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The logic of the argument is easy to follow.
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Various techniques (approximations, numerical results, and exact results) are used effectively to shed light on the problem from several angles and answer the questions raised.
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The presentation of the figures is of great quality.
Weaknesses
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(Very few) typos
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Caption of fig.1 may be improved (see below).
Report
Requested changes
I suggest that authors take these few comments into account. archetypical (or rather archetypal ?) (Col.1, page 2) (Rare) inconsistent mixing of British and American spelling : most of the time UK ( flavour, characterises, dimerised, minimise, renormalises... ) but occasionally US (discretization, quantized, symmetrization, delocalizes...) operatros -> operators (fig 1 caption) ingoing indices -> incoming indices (col.2 page 9) (Outgoing is ok) subschains -> subchains (fig 13 caption) substraction -> subtraction (fig 15 caption) Dashed lines are not documented and maybe few words should be added concerning the rung basis (defined in section IV.A) to make the caption more self-contained.1.Typos
2. Caption of Figure 1
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)