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Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
by Yuan Miao, Enej Ilievski, Oleksandr Gamayun
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Submission summary
| Authors (as registered SciPost users): | Oleksandr Gamayun · Yuan Miao |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2010.07232v4 (pdf) |
| Date submitted: | Nov. 10, 2020, 10:40 a.m. |
| Submitted by: | Miao, Yuan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Using the algebro-geometric approach, we study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear spin waves governed by the anisotropic Landau-Lifshitz equation arise as coherent macroscopic low-energy fluctuations of the ferromagnetic grounds state. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves. To resolve their internal magnon structure, we carry out the semi-classical quantisation of classical spin waves using the Riemann-Hilbert problem approach. We describe overlaps of semi-classical eigenstates employing functional methods and correlation functions of these states with aid of classical phase-space averaging.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2020-12-29 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2010.07232v4, delivered 2020-12-29, doi: 10.21468/SciPost.Report.2343
Strengths
- Thorough analysis supported by numerics
- Complete classification of semi-classical states of the XXZ spin chain
- Many examples considered in detail
Weaknesses
- none
Report
The paper can be published as is, but I believe it will benefit from a few minor improvements.
Requested changes
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What determines the spacial period of the solution? From the discussion on p.20 and eqs. 4.43, 4.44 it seems to be the asymptotics of the quasi-momentum at infinity. This is indeed the case for the 1-cut solution, but for the 2-cut case the period depends on moduli. Why?
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The authors call nj winding numbers and mode intermittently. These are physically distinct notions. The term better reflecting the physics should be used uniformly.
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Deviations of the σzσz correlator in fig. 11b from 8.5 are way too large to be accounted for by finite-size effects, if estimated from σxσx where the agreement is almost perfect. This difference needs to be explained, or else the authors should provide a reliable estimate of finite-size corrections. Otherwise the discrepancy casts doubts on the conjectural relation between the phase average and quantum correlators.
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Limits of integration in 2.38 and 2.41 are inverted.
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I'd suggest to proofread the text English-wise.
Report #1 by Anonymous (Referee 1) on 2020-12-4 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2010.07232v4, delivered 2020-12-04, doi: 10.21468/SciPost.Report.2253
Strengths
Pedagogically written
Carefully written
Important results