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Hidden order in dielectrics: string condensation, solitons, and the charge-vortex duality
by Sergei Khlebnikov
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Sergei Khlebnikov |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202411_00025v1 (pdf) |
| Date submitted: | Nov. 13, 2024, 8:08 p.m. |
| Submitted by: | Sergei Khlebnikov |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Description of electrons in a dielectric as solitons of the polarization field holds promise as a method for computer simulations of the dynamics of excited states. For that description to be realistic, the interaction between the solitons (prior to their coupling to electromagnetism) must be short-ranged. We present an analytical study of the mechanism by which this is achieved. It is unusual in that it enables screening of the electrically neutral soliton cores by polarization charges. We also argue that the structure of the solitons allows them to be quantized as either fermions or bosons. At the quantum level, the theory has, in addition to the solitonic electric, elementary magnetic excitations, the quantization of which results in an additional (``topological") contribution to the magnetic susceptibility. In the ground state of a typical dielectric, the effect is weak, but we suggest that it may be enhanced in radiatively excited states of small crystals.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
2 – It connects different branches of physics and is clearly written to a large extent.
Weaknesses
2 – It remains unclear why any of the discussed phenomena have not yet been seen experimentally. For instance, the manuscript lacks a realistic estimate of the parameter mu, which represents the spatial extent of the soliton.
Report
On the other hand, the manuscript is partially elusive concerning possible experimental signatures of the conjectured description of electrons. Prospects for observing the proposed quantized magnetic vortices in a dielectric are discussed. But it remains unclear which order of magniture the screening parameter mu might have, which represents a key property of the underlying theory. And it is vaguely mentioned that solitons can be quantized either as bosons or fermions in 3D, or as anyons in 2D. Any discussion about how this conclusion affects the experimental detection is lacking.
Requested changes
1 – Elaborate further on the experimental observability.
2 – Make the manuscript self-contained by considering to merge the manuscript with unpublished Ref. [2].
Recommendation
Ask for major revision
Strengths
1- The manuscript is written in an overall clear, high-quality English. 2- The article provides a mathematically rigorous description of electrons in a dielectric medium in terms of solitons, and of the arising screening mechanism. 3-The author dedicates a whole section to the discussion of experimental evidences of emergent quantized magnetic excitations, with some emphasis on a possible experimental platform for the measurement of these effects.
Weaknesses
1- On too many instances, the author either introduces notations or equations without definition, proper physical motivation or reference to the litterature. 3- The article lacks an Appendix.
Report
The results presented in this article and their insightful discussion by the author show, in my opinion, a high degree of relevance to the physics of dielectric media. The mathematical rigor of their derivation also contributes to the good readability of the article. My only criticism concerns the lack of physical motivation of certain equations, which are introduced without justification. Similarly, the author has sometimes made statements without supporting them. In this sense, the absence of an appendix providing further details and filling in these gaps is particularly detrimental.
Provided that the author corrects these flaws and introduces an appendix to their manuscript, I would support publication in SciPost Physics.
Requested changes
1- In the introduction, 4th line of the 2nd paragraph: "stings"-> "strings" 2- Could the author provide a justification for the form taken by Eq (2), especially the dependence in the divergence of the polarization field. 3- Could the author please explicitate why "the precise form of $V(p)$ is not tooimportant here", right before Eq (3). 4- In Eq (20) and (22)-(23), please define the function $K_n$. 5- Following Eq (23), the author claims that one can fix $\tilde\phi=0$, please provide a proof in appendix. 6-Please provide in appendix the full derivation of Eq. (32). 7- Justify the form taken by the action $S_E$ introduced in Eq. (43). 8- Provide a derivation of Eq (44).
Recommendation
Ask for minor revision