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Strongly-interacting bosons at 2D-1D Dimensional Crossover

by Hepeng Yao, Lorenzo Pizzino, Thierry Giamarchi

Submission summary

Authors (as Contributors): Thierry Giamarchi · Hepeng Yao
Submission information
Arxiv Link: (pdf)
Date submitted: 2022-09-28 07:58
Submitted by: Yao, Hepeng
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Experiment
  • Atomic, Molecular and Optical Physics - Theory
  • Quantum Physics
Approaches: Theoretical, Computational


We study a two dimensional (2D) system of interacting quantum bosons, subjected to a continuous periodic potential in one direction. The correlation of such system exhibits a dimensional crossover between a canonical 2D behavior with Berezinski-Kosterlitz-Thouless (BKT) properties and a one-dimensional (1D) behavior when the potential is large and splits the system in essentially independent tubes. The later is in the universality class of Tomonaga-Luttinger liquids (TLL). Using a continuous quantum Monte Carlo method, we investigate this dimensional crossover by computing longitudinal and transverse superfluid fraction as well as the superfluid correlation as a function of temperature, interactions and potential. Especially, we find the correlation function evolves from BKT to TLL type, with special intermediate behaviors appearing at the dimensional crossover. We discuss how the consequences of the dimensional crossover can be investigated in cold atomic gases experiments.

Current status:
Awaiting resubmission

Submission & Refereeing History

Reports on this Submission

Anonymous Report 1 on 2022-10-22 (Invited Report)


The manuscript meets the acceptance criterion, as the results are sound and have direct implications to experiments.


  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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Anonymous on 2023-01-18  [id 3246]

The manuscript studies with the quantum Moneta Carlo method strongly-interacting bosons by subjecting them to a periodic potential in one direction. Depending on the transversal tunneling the system shows a dimensional crossover between a 2D behavior with BKT properties and a 1D behavior of the Tomonaga Luttinger liquid. The manuscript is concisely written and presents various interesting results, which characterize the emerging dimensional crossover. In view of possible experimental realizations of such a dimensional crossover in the realm of atomic quantum gases, these theoretical findings are important. Therefore, the manuscript should be published in SciPost Physics journal.

However, the authors should revise their manuscript by taking into account the following criticism. The BKT physics at finite V_y, when the superfluid becomes anisotropic, needs further analysis:

a) On page 7 the BKT critical temperature at V_y = 0 Er is compared with the quantum Monte Carlos results, which corresponds to the 2D regime. Here the question arises which BKT critical temperature emerges at a finite potential depth V_y, when the superfluidity becomes anisotropic. And how this BKT critical temperature compares with the results from the quantum Monte Carlo simulations.

b) Similar questions arise for Fig. 4(b2) and 4(c2). Does the power-law obtained from quantum Monte Carlos agree with the BKT predictions for the anisotropic superfluid regime?

Apart from that the authors should improve their manuscript along the following lines:

1) Abstract: The later is in the universality class → The latter is in the universality class

2) Page 2: The references [6, 33–36] could be extended by adding

P. Christodoulou, M. Gałka, N. Dogra, R. Lopes, J. Schmitt, and Z. Hadzibabic: Observation of first and second sound in a BKT superfluid, Nature 594, 191-194 (2021)

3) Page 4: Instead of the unprecise comment

see detailed calculations in the appendix

it would be preferable to mention explicitly in which part of the Appendix this information is available. This also applies to other parts of the manuscript where only Ref. [50] is cited.

4) Caption of Fig. 2: and they follows a fit → and they follow a fit

5) Page 5: we can judge crossover potential -> we can judge the crossover potential

6) Page 6: These parameters allows us –> These parameters allow us

7) Caption of Fig. 4: Subfigures (a1)-(d1) shows -> Subfigures (a1)-(d1) show

8) Page 9: by the ground state of harmonic oscillator. -> by the ground state of the harmonic oscillator.

Matthew Davis  on 2023-01-19  [id 3249]

(in reply to Anonymous Comment on 2023-01-18 [id 3246])

As editor in charge of this submission, I note that this comment was submitted by one of the invited referees.