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Mobile impurities in integrable models
by Andrew S. Campbell, Dimitri M. Gangardt
This is not the latest submitted version.
This Submission thread is now published as
|As Contributors:||Dimitri Gangardt|
|Arxiv Link:||http://arxiv.org/abs/1701.00810v2 (pdf)|
|Date submitted:||2017-04-26 02:00|
|Submitted by:||Gangardt, Dimitri|
|Submitted to:||SciPost Physics|
We use a mobile impurity or depleton model to study elementary excitations in one-dimensional integrable systems. For Lieb-Liniger and Yang-Gaudin models we express two phenomenological parameters characterising renormalised inter- actions of mobile impurities with superfluid background: the number of depleted particles, $N$ and the superfluid phase drop $\pi J$ in terms of the corresponding Bethe Ansatz solution and demonstrate, in the leading order, the absence of two-phonon scattering resulting in vanishing rates of inelastic processes such as viscosity experienced by the mobile impurities
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Author comments upon resubmission
calculations of effective interactions parameters (collective charges) of a
mobile impurity (depleton) model. We mention their relation to the edge
exponents in various correlation functions, but Section 2 in the previous
version, containing extended derivation of the correlation functions'
asymptotics, is moved now to Appendix A.
We now clearly state which results were obtained previously and give
appropriate credit. We still feel, however, that for the sake of completeness
and reader's convenience, these results should be included in the manuscript
and we state this in the text.
List of changes
* Title and abstract changed
* Introduction rewritten
* Section 2 moved to Appendix A
* Credit to previously obtained results is given throughout the paper.
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 4 on 2017-5-31 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1701.00810v2, delivered 2017-05-31, doi: 10.21468/SciPost.Report.153
As in the first report
Some citations are strange.
The authors did implement many of the referees' suggestions what has improved the paper. However, they also did made some quite queer amendments, especially in what concerns the bibliography and the citations.
In the present version, there is no mention -with the exception of reference 37- of all the efforts that where made within the integrable model community regarding to the calculation of correlation functions and extractions of the edge exponents, at least in some regimes.
The authors already did provide some citations in the first version of the paper and I have suggested some other literature, so as to provided a fairer picture. Since, in fine, the author's work relies directly on integrable techniques, I believe that making such an omission is unfair.
The authors inaccurately describe the content of certain papers. To be more precise:
In the middle of page 3, the authors discuss the goal of their paper. There they claim that their result "reproduces the conjectured identity of chiral linear combinations of the collective charges, so called chiral phase shifts, with BA shift functions".
This is not true. Paper 37 expresses the edge exponents in terms of shift functions by arguing directly that phase shifts in the unitary transform should be given by the same formula as for non-interacting fermions, and this is enough for their calculation.
The works 22,36 identify the coupling constants in their effective Hamiltonian by comparing their low-energy spectrum with the one issuing from the Bethe Ansatz. By the way, the authors do not prove the predictions issuing, per se, from the work 36 since it deals with the XXZ chain which is not considered in the author's paper.
I stress that, all these works directly provide an expression for the edge exponents in terms of the shift function. Thus, 37 and 38 provide the same expression for the edge exponents.
What the authors do is to prove the expressions for the phase shifts that were argued to hold in ref. 23 and in "Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit" by A. Imambekov and L.I.Glazman. Curiously, that last paper is not cited in the present version of the paper while it was cited in the first one.
Page 4 The authors attribute to 14 the proposal of the relations (3)-(4). However that paper dates to 2012 while "Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit" appeared in 2009, just as reference 23. Again, true, the expressions obtained there are written in another language but I believe that the correspondence between the two is not that hard.
Below (60). The identity was conjectured to hold much much earlier than . However, the work  was the first to establish it.
See, e.g. "Conformal dimensions in Bethe ansatz solvable models" in what concerns the nested Bethe ansatz case.
Anonymous Report 3 on 2017-5-25 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1701.00810v2, delivered 2017-05-25, doi: 10.21468/SciPost.Report.149
In their work, Campbell and Gangardt re-derive some important results of the theory of Nonlinear Luttinger liquids. Most notably, they re-affirm the absence of viscosity for excitations describing the edge of the spectral continuum in two specific integrable models: the Lieb-Liniger model and the Yang-Gaudin model for BOSONS with spin 1/2.
While there is little new physics in their work, I believe it is methodically useful and should be published in SciPost. The previous Referees already fought heavily for assigning the proper credit to various groups, so I spare the Authors from some minor grievances.
I have two specific requests to the Authors:
(1) In the Introduction (p. 3), please substantiate of modify the phrase: "The equivalence
of these results to those obtained in Ref.  using phenomenological mobile impurity model
relies on the conjectured relation between the collective charges and BA shift functions which
we demonstrate here." It is not clear how the notion of "collective charges" was involved in demonstrating the equivalence.
(2) It seems to me that the Authors consider only the bosonic Yang-Gaudin model. If this is the case, that must be clearly stated in the beginning of the manuscript and repeated in the main text in the sections devoted to that model.
I hope the Authors introduce changes adequately addressing these two comments.
Anonymous Report 2 on 2017-5-23 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1701.00810v2, delivered 2017-05-23, doi: 10.21468/SciPost.Report.146
Nicely written paper containing important results.
No obvious weaknesses.
The authors have responded adequately to the questions raised by the referees in the first round. I recommend the paper for publication.
No changes required.
Anonymous Report 1 on 2017-4-27 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1701.00810v2, delivered 2017-04-27, doi: 10.21468/SciPost.Report.123
1. The paper contains new important results.
1. I do not see evident weaknesses.
I appreciate the changes made by the authors and recommend the manuscript for publication.
1. No changes required.