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Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas

by Giulia De Rosi, Riccardo Rota, Grigori E. Astrakharchik, Jordi Boronat

This Submission thread is now published as

Submission summary

Authors (as Contributors): G. E. Astrakharchik · Giulia De Rosi · Riccardo Rota
Submission information
Arxiv Link: (pdf)
Data repository:
Date accepted: 2022-07-21
Date submitted: 2022-05-24 11:44
Submitted by: De Rosi, Giulia
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Experiment
  • Atomic, Molecular and Optical Physics - Theory
Approaches: Theoretical, Computational


We reveal an intriguing anomaly in the temperature dependence of the specific heat of a one-dimensional Bose gas. The observed peak holds for arbitrary interaction and remembers a superfluid-to-normal phase transition in higher dimensions, but phase transitions are not allowed in one dimension. The presence of the anomaly signals a region of unpopulated states which behaves as an energy gap and is located below the hole branch in the excitation spectrum. The anomaly temperature is found to be of the same order of the energy of the maximum of the hole branch. We rely on the Bethe Ansatz to obtain the specific heat exactly and provide interpretations of the analytically tractable limits. The dynamic structure factor is computed with the Path Integral Monte Carlo method for the first time. We notice that at temperatures similar to the anomaly threshold, the energy of the thermal fluctuations become comparable with the maximal hole energy, leading to a qualitative change in the structure of excitations. This excitation pattern experiences the breakdown of the quasi-particle description for any value of the interaction strength at the anomaly, similarly to any superfluid phase transition at the critical temperature. We provide indications for future observations and how the hole anomaly can be employed for in-situ thermometry, identifying different collisional regimes and understanding other anomalies in atomic, solid-state, electronic, spin-chain and ladder systems.

Published as SciPost Phys. 13, 035 (2022)

List of changes

Changes to the text are marked in the file:

A list of main changes follows:

1) New text close to the end of Sec. 5 on the change of the behavior of the Dynamic Structure Factor (DSF) upon request of Report 1.

2) Small changes to the text about the definition of anomaly in Secs. 1, 4.1, 7 and caption of Fig. 3 upon request of Report 1.

3) Changes to the text related to the breakdown of the quasiparticle picture in Secs. 1, 5 and 7 upon the suggestion of Report 1.

4) New comment in Sec. 3 about the importance of approximated limits of the specific heat for the interpretation of Fig. 1 as a diagram of regimes following the point raised in Report 2.

5) We have deleted “continuous” when referred to the spectrum in Secs. 1, 4, and 7 following the point raised in Report 2.

6) We have listed the kinds of many-body systems whose anomalies may be simulated by our hole anomaly, after the comment in Report 2.

7) New sentence about the measurement of the chemical potential for temperatures below and above the hole anomaly in Sec. 7 following the comment of Report 2.

8) New paragraph about spin chains and ladders in Sec. 7 with the inclusion of references suggested by Referee 3. New reference to spin ladders in the Abstract, upon the great suggestion of Report 3.

9) Change of the Acknowledgements Section, with the inclusion of Referee 3.

10) New Appendix about the simulated annealing which is the method employed for the calculation of the DSF and reference to it at the end of Sec. 6 upon request of Report 3.

11) New comment in Sec. 7 with the comparison of DMRG and PIMC techniques, upon request of Report 3.

Reports on this Submission

Anonymous Report 3 on 2022-6-23 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2104.12651v4, delivered 2022-06-23, doi: 10.21468/SciPost.Report.5272


The modifications made by the authors have addressed my previous comments. In particular there is now a satisfactory discussion of the observed anomaly in a broader context, connecting also the calculations to more intuitive explanations. The discussion on the monte-carlo part has also been improved.

In connection with my previous comments on the scientific qualities of the papers and the results, I think that the current version is now perfectly adapted for publication in SciPost Physics and I do recommend publication in its present form.

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

Anonymous Report 2 on 2022-6-8 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2104.12651v4, delivered 2022-06-08, doi: 10.21468/SciPost.Report.5208


- An interesting study of the properties of a 1D integrable quantum model at finite temperature.

- A combination of different techniques to compute key observables, including the Bethe ansatz (specific heat) and the path-integral Monte Carlo (dynamic structure factor).

- A physical interpretation of the anomaly in the specific heat for the Lieb-Lininger model.


The authors have provided a detailed and honest answer to all my remarks and criticisms. The presentation of the results has also been significantly improved, including a discussion on the procedure used to extract the anomaly temperature T_A from the specific heat numerical data.
The manuscript contains new and interesting results of one-dimensional integrable models at finite temperature. I therefore recommend publication in SciPost Physics.

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

Anonymous Report 1 on 2022-6-7 (Invited Report)


The authors have not really addressed many of my concerns in their revised version. Most importantly they have not addressed my comment 1), namely that as the free Fermi gas displays the same behavior discussed in the manuscript the scale identified by the authors should simply have a kinematic origin. I also find their reply to my comment 4) about the claimed similarities between the "anomaly" and a phase transition very strange: the free Fermi gas displays this behavior and surely does not have a phase transition.

I do not think that the revised version satisfies the stringent publication criteria of SciPost Physics, but it would be suitable for SciPost Physics Core.

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

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