SciPost Submission Page
Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting
by Dung Xuan Nguyen, Andrey Gromov, Sergej Moroz
This is not the current version.
|As Contributors:||Sergej Moroz · Dung Nguyen|
|Arxiv Link:||https://arxiv.org/abs/2005.12317v2 (pdf)|
|Date submitted:||2020-06-23 02:00|
|Submitted by:||Nguyen, Dung|
|Submitted to:||SciPost Physics|
Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.
Submission & Refereeing History
You are currently on this page
Reports on this Submission
Anonymous Report 2 on 2020-9-27 Invited Report
The MS uses the techniques that recently became popular to study the classical problem of melting and structure of vortex lattice in a superfluid system at zero temperature. The MS describes the interaction between defects in such a lattice and reports to be short-range, both attractive and repulsive. The MS also discusses the condensation of the defects and supersolidity.
The MS refers to duality discussion in the context of supersolid Helium Ref 32. I think the way it is formulated is misleading because standard supersolidity in Helium was disproven and corresponding claims in experimental articles retracted by Chan et al in follow-up papers. One may still call supersolid the superfluid dislocation but not in the same sense. Here the presentation should be made more accurate.
The authors also refer to superfluid in the magnetic field. This is not a real magnetic field that the authors consider. The corresponding formulations could be better.
The term magneto-crystal appears without definition.
In my opinion, the MS makes, in my opinion, an unjustified bold claim about realization:
"This setup can be realized and investigated in nowadays cold atom experiments." These systems have trap potential. Although box traps are possible, they are finite, and it is difficult to achieve a rapid rotation. Could the authors justify that better or soften the formulation?
Apart from these minor comments, I think it is very good work that should be published.
Anonymous Report 1 on 2020-9-20 Invited Report
This paper contains an impressive discussion and derivation of a dual theory of melting of a vortex crystal in a two-dimensional quantum boson fluid. Perhaps the only missing ingredient is a renormalization group (RG) analysis, similarly to the one employed in the classical field theory of crystal melting, as discussed long time ago by B. Halperin and D. Nelson and by Kleinert in Ref. 31. A generalization of these ideas for a non-relativistic quantum system would be desirable, but not required for this manuscript.
I did not find any obvious flaw in this manuscript and so I don't judge any changes to be necessary. Perhaps the authors can also include in the literature some other earlier works on the classical, non-fractonic counterpart, like Nelson, Young, and others, who also show the subtleties involved when an RG analysis is performed, which is akin to the one in BKT systems. Kleinert's book cited in Ref. 31 included a thorough reference account and references to these earlier works.