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Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices

by J. A. Koziol, G. Morigi, K. P. Schmidt

Submission summary

Authors (as registered SciPost users): Jan Alexander Koziol · Kai Phillip Schmidt
Submission information
Preprint Link:  (pdf)
Data repository:
Date submitted: 2023-11-20 14:09
Submitted by: Koziol, Jan Alexander
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state results from the interplay between the lattice geometry and the long-range interactions, which we account for by means of a classical spin mean-field approach limited by the size of the considered unit cells. This extended classical spin mean-field theory accounts for the long-range density-density interaction without truncation. We consider three different lattice geometries: square, honeycomb, and triangular. In the limit of zero hopping the ground state is always a devil's staircase of solid (gapped) phases. Such crystalline phases with broken translational symmetry are robust with respect to finite hopping amplitudes. At intermediate hopping amplitudes, these gapped phases melt, giving rise to various lattice supersolid phases, which can have exotic features with multiple sublattice densities. At sufficiently large hoppings the ground state is a superfluid. The stability of phases predicted by our approach is gauged by comparison to the known quantum phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as well as quantum Monte Carlo simulations for the dipolar case on the square lattice. Our results are of immediate relevance for experimental realisations of self-organised crystalline ordering patterns in analogue quantum simulators, e.g., with ultracold dipolar atoms in an optical lattice.

Current status:
Awaiting resubmission

Reports on this Submission

Anonymous Report 2 on 2024-2-26 (Invited Report)


1) The manuscript is clearly written. A brief review of the method used is provided. All relevant physics is neatly summarized in the first sections of the manuscript.

2) Citations are carefully chosen and very relevant to the topic.

3) Results are for the most part clearly described.

4) The results of this work are interesting and relevant to current experiments with ultracold gases.

5) The manuscript provides novel in depth analysis of the strongly interacting regime (where the method presented in most accurate). A plethora of solid phases are presented which had not been observed before with approximation-free methods.


1) On the one hand, significant emphasis is given to QUANTUM phases, such as supersolid phases, in the introductory part of the manuscript. On the other hand, most of the description of results is dedicated to solid phases. Only supersolid phases at 1/2 (for bipartite) and 1/3,1/4 (for non-bipartite) are marked in the phase diagrams. While the 1/4 supersolid in triangular lattice is new, the others were already known. It would be better to further describe novel supersolids such as the ones mentioned for square lattice (for honeycomb lattice limitations of the method are discussed). For example, what are supersolids "with more complex sub lattice structure"? Maybe a picture of density patterns of this supersolid would help. If it is already there, then it is not clear that it does refer to a supersolid phase. Moreover, the authors should comment about how their results compare with QMC study of hard-core purely repulsive dipolar bosons in triangular lattice (PRL 104, 125302 (2010)).


Overall, this is an interesting, well-written manuscript which presents results on many-body hamiltonians relevant to current experimental efforts in ultracold gases. It meets the criteria for publication of SciPost and I therefore recommend it for publication once the requested changes are addressed.

Requested changes

1) Do authors have an explanation on why their method does not compare as well with approximation-free numerical methods in the case of non-bipartite triangular lattice?

2) Why is the method so much more accurate at the Heisenberg point?

3) Can the authors address the point mentioned in the Weaknesses Section of this report?

  • validity: high
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Anonymous Report 1 on 2024-2-2 (Invited Report)


1) A detailed mean-field analysis of dipolar bosons particularly in a triangular lattice where QMC data does not exist.


1) The paper seems to be a possible and somewhat expected application of the formalism developed in Ref 34 of the work (by the same authors).

2) The mean field phase diagrams of dipolar bosons has been worked out by several authors in the phase predicting existence of supersolid phase and
devil staircase structures. See for example Phys. Rev. A 83, 013627 (2011), New J. Phys. 17 123014 (2015) or Europhys. Lett. 87 36002 (2009). In fact there are many other similar results in the literature.


I believe, based on the weaknesses mentioned, the paper in its present form is suitable for publication in Scipost Phys. Core. Whereas the analysis is detaiked and it deserves publication in some form, I do not see sufficiently new results which allows consideration in Scipost.

  • validity: good
  • significance: ok
  • originality: ok
  • clarity: good
  • formatting: good
  • grammar: excellent

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