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Effective field theory of a vortex lattice in a bosonic superfluid
by Sergej Moroz, Carlos Hoyos, Claudio Benzoni, Dam Thanh Son
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|As Contributors:||Sergej Moroz|
|Arxiv Link:||https://arxiv.org/abs/1803.10934v2 (pdf)|
|Date submitted:||2018-05-22 02:00|
|Submitted by:||Moroz, Sergej|
|Submitted to:||SciPost Physics|
Using boson-vortex duality, we formulate a low-energy effective theory of a two-dimensional vortex lattice in a bosonic Galilean-invariant compressible superfluid. The excitation spectrum contains a gapped Kohn mode and an elliptically polarized Tkachenko mode that has quadratic dispersion relation at low momenta. External rotation breaks parity and time-reversal symmetries and gives rise to Hall responses. We extract the particle number current and stress tensor linear responses and investigate the relations between them that follow from Galilean symmetry. We argue that elementary particles and vortices do not couple to the spin connection which suggests that the Hall viscosity at zero frequency and momentum vanishes in a vortex lattice.
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Anonymous Report 2 on 2018-7-17 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1803.10934v2, delivered 2018-07-17, doi: 10.21468/SciPost.Report.536
1. A novel formulation of the low energy theory of the vortex lattice, which allows a systematic expansion beyond leading order.
2. A calculation of the Hall viscosity for the vortex lattice, backed up by careful general arguments.
1. Much of the presentation involves the recovery of existing results. At times it is unclear what is new and what is known.
This is an interesting paper that makes advances in the understanding of the low-energy theory of vortex lattices in compressible superfluids. While this topic is one that has a long history, the authors are clear to cite previous works which are closely related. In particular, they show that their effective theory is equivalent to that of Ref .
The authors emphasize that, despite this equivalence, their approach allows a systematic construction of corrections to the leading order theory. They provide descriptions of (some of) these next to leading order corrections. They also compute the response functions, and present general features expected from Galilean invariance.
Importantly, the authors calculate the Hall viscosity and argue on general grounds that it should vanish.
The paper makes useful advances in the field. In order to clarify the presentation, and the significance of their new results, I ask that the authors address the suggested changes below.
1. On page 4, following Eqn (2), it would be helpful for the reader if the authors could contrast the density and current in their dual formulation with the more familiar expressions in terms of the superfluid phase (e.g. in Ref. ). I know that a detailed discussion of Ref.  is provided in the appendix. However, since page 4 is still largely introductory material, adding some targeted explanations here would be an important addition to help familiarize the reader with the meaning of the dual formulation.
2. Please indicate more clearly which of the results are known, and to what extent the results match. For example, the text around Eqn (12) implies that the $k^2$ behavior is known; but does the prefactor not also match previous results? Do Eqns (14,16,17,18) appear in the literature? If expressions in the literature exist for these quantities, but differ in detail, please comment on this as well as the reasons for any difference.
3. Just before Eqn (16), typo: "the the"
4. In Section VII, the authors provide detailed arguments for the vanishing of the Hall viscosity. As they also point out in the Discussion, Sec VIII, different result applies for chiral vortex fluids. Where did the arguments of VII fail for the chiral vortex fluid? It would be helpful to insert a comment on this at the appropriate place in Sec VII.
Anonymous Report 1 on 2018-7-16 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1803.10934v2, delivered 2018-07-16, doi: 10.21468/SciPost.Report.535
1) The manuscript formulates an effective field theory of a vortex lattice from the boson-vortex duality perspective. This formulation has the potential to go beyond the hydrodynamic approach.
2) The manuscript raises several very interesting questions, especially those related to the Hall viscosity, motivating the future research.
1) The results on the excitation spectrum of a vortex lattice in a compressible superfluid are not new.
2) The claim of the absence of the Hall viscosity in a vortex lattice is not rigorous. However this point can be also viewed as a strength because it may motivate new research directions.
Please see the attached file.
Please see the attached file.