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Systematic Analysis of Crystalline Phases in Bosonic Lattice Models with Algebraically Decaying Density-Density Interactions
by J. A. Koziol, A. Duft, G. Morigi, K. P. Schmidt
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|Authors (as registered SciPost users):||Antonia Duft · Jan Alexander Koziol|
|Preprint Link:||https://arxiv.org/abs/2212.02091v1 (pdf)|
|Date submitted:||2022-12-06 11:04|
|Submitted by:||Koziol, Jan Alexander|
|Submitted to:||SciPost Physics|
We propose a general approach to analyse diagonal ordering patterns in bosonic lattice models with algebraically decaying density-density interactions on arbitrary lattices. The key idea is a systematic search for the energetically best order on all unit cells of the lattice up to a given extent. Using resummed couplings we evaluate the energy of the ordering patterns in the thermodynamic limit using finite unit cells. We apply the proposed approach to the atomic limit of the extended Bose-Hubbard model on the triangular lattice at fillings $f=1/2$ and $f=1$. We investigate the ground-state properties of the antiferromagnetic long-range Ising model on the triangular lattice and determine a six-fold degenerate plain-stripe phase to be the ground state for finite decay exponents. We also probe the classical limit of the Fendley-Sengupta-Sachdev model describing Rydberg atom arrays. We focus on arrangements where the atoms are placed on the sites or links of the Kagome lattice.
Submission & Refereeing History
- Report 3 submitted on 2023-03-23 04:30 by Anonymous
- Report 2 submitted on 2023-03-13 13:02 by Anonymous
- Report 1 submitted on 2023-03-10 02:53 by Anonymous
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Reports on this Submission
- Cite as: Anonymous, Report on arXiv:2212.02091v1, delivered 2023-02-06, doi: 10.21468/SciPost.Report.6691
1. The work is experimentally relevant, theoretically sound, and the manuscript is also well-written and straightforward to follow.
2. I personally believe that these results, even though classical, would be extremely useful to the ultracold-atoms community because the solid density-wave-ordered states may be regarded as starting points both to benchmark experiments and to incorporate quantum corrections.
3. Moreover, there are often subtle effects from the long-ranged dipolar ($1/r^3$) or van der Waals ($1/r^6$) interactions, which are hard to quantify in simple mean-field calculations, and the careful analysis outlined in this paper bridges this gap.
Please refer to the attached PDF.
I would recommend publication in SciPost Physics after some revisions (listed in the report).
Please refer to the attached PDF.
- Cite as: Anonymous, Report on arXiv:2212.02091v1, delivered 2023-01-31, doi: 10.21468/SciPost.Report.6644
1- This paper provides a systematic algorithm to determine the charge order for lattice classical models with power-law density interactions.
2- Such an analysis provides a good starting point to consider quantum effects (i.e. off-diagonal terms in the Fock basis)
1- It is limited to weak long-range interactions.
2- There is no study of any quantum case although several such models are mentioned.
I find the paper particularly pedagogical and well written. It is nice to see a systematic method to tackle classical models and find the lowest energy pattern. In fact, it is a bit surprising that such a method has not been proposed before ?
Regarding the motivations, there are several quantum models (and references about them), but in its current form, the paper only consider the classical limit. This would be much more interesting if some precise connections could be made to quantum models.
1- I would suggest to remove lots of quantumness from the abstract and the body of the paper. Indeed, the quantum statistics plays no role in the current study, so that it would apply equivalently to bosons, fermions or classical objects.
2- Is it possible to consider, at least partly, the long-range case as done when using Ewald summation ?
3- I would suggest to remove most references about quantum experiments, quantum phases (superfluids, super solids) which are not relevant to the present study.
- Cite as: Anonymous, Report on arXiv:2212.02091v1, delivered 2022-12-30, doi: 10.21468/SciPost.Report.6407
1. The authors provide a computational mechanism to identify ground states of quantum systems with long-range potentials in the classical limit where the off-diagonal terms in the computational basis (for example Fock basis in real space) is ignored.
2. The states found using this method could be a good starting point for addressing effect of quantum fluctuations for such systems.
3. The treatment, applied to Rydberg atoms on links of Kagome lattice, finds a somewhat different picture than was found earlier in Ref 97 of the paper. In particular they notice absence of resonatiing plaquettes which may call into question the spin liquid state found earlier. If correct, this is expected to open up further studies in the field.
1. The authors could have studied effect of the off-diagonal terms on their analysis (perturbatively and numerically) rather than leaving this for a future study. That would have provided a more complete picture.
Overall, the authors provide a computational scheme which may be used to numerically evaluate the ground state configuration of a quantum system with long-range density-density or spin-spin interaction in the classical limit. This method is interesting and may be useful for accurate determination of ground states of such systems. However, they have not estimated the effect of off-diagonal terms ( which are almost always present and important) on their analysis. If this issue can be taken care of (even perturbatively and numerically
for, say, the rydberg atoms on Kagome), the paper shall be much stronger and I would certainly recommend it for publication.
1. It would be nice to have a perturbative and numerical treatment of off-diagonal terms. If this is really impossible, a discussion regarding why that is the case should be included. This is particularly improtant for the Rydberg atoms array on Kagome lattice links.