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On quantum melting of superfluid vortex crystals: from Lifshitz scalar to dual gravity
by Dung Xuan Nguyen, Sergej Moroz
Submission summary
| Authors (as registered SciPost users): | Sergej Moroz · Dung Nguyen |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2310.13741v2 (pdf) |
| Date submitted: | 2024-03-12 12:26 |
| Submitted by: | Moroz, Sergej |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Despite a long history of studies of vortex crystals in rotating superfluids, their melting due to quantum fluctuations is poorly understood. Here we develop a fracton-elasticity duality to investigate a two-dimensional vortex lattice within the fast rotation regime, where the Lifshitz model of the collective Tkachenko mode serves as the leading-order low-energy effective theory. We incorporate topological defects and discuss several quantum melting scenarios triggered by their proliferation. Furthermore, we lay the groundwork for a dual non-linear emergent gravity description of the superfluid vortex crystals.
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The authors aim to provide a low-energy description of vortex crystals. The paper is well-written, with a clear objective. However, I have several concerns that, if addressed, could further improve the clarity and readability of the paper:
1. The connection between gauge symmetry and glide constraints is not clearly justified. Typically, glide constraints are associated with the requirement to prevent volume changes. In a systematic low-energy theory, I would expect the displacement field to introduce a massive Goldstone mode for conformal transformations, which is subsequently eliminated by a constraint ensuring quadrupole conservation. It is unclear why this would be linked to gauge symmetry.
2. The advantage of replacing the symmetric tensor gauge field with the metric is not apparent.
3. The physical significance of the velocity field remains opaque. The same is true for the manifold described by the metric constructed out of $A_{ij}$ and the diffeomorphism invariance that follows.
4. I do not see why I should use the metric to raise indices. One does not use the field $A_{ij}$ for that purpose.
5. Do defects play any role in the curvature of the Riemann tensor introduced in Section 4?
6. The omission of torsion in the discussion is puzzling.
7. The authors mention the bimetric theory of gravity, presumably drawing on their experience with the Quantum Hall Effect. However, any viscoelastic gapless medium inherently introduces an additional metric due to elastic degrees of freedom. It is uncertain whether the authors would refer to this theoretical approach as 'bimetric' in a general sense or if 'bimetric theory' has a more specific, technical definition that is not addressed in the paper.
8. The prevailing view is that the strain tensor in elasticity couples to the metric as a Higgs field breaking translations on curved manifolds. This is a modern realization of Kleinert ideas, known in the literature. However, I find it difficult to see how the methods introduced in this paper relate to these established models of embedding crystals into curved manifolds.
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