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Hilbert Space Structure and Classical Limit of the Low Energy Sector of U(N) Quantum Hall Ferromagnets
by Manuel Calixto, Alberto Mayorgas and Julio Guerrero
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Submission summary
| Authors (as registered SciPost users): | Manuel Calixto · Julio Guerrero · Alberto Mayorgas |
| Submission information | |
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| Preprint Link: | scipost_202212_00029v1 (pdf) |
| Date submitted: | 2022-12-15 16:44 |
| Submitted by: | Calixto, Manuel |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022) |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify and construct the Hilbert space of the low energy sector of U(N ) quantum Hall/Heisenberg ferromagnets at filling factor M for L Landau/lattice sites. The carrier Hilbert space of irreducible representations of U(N ) is described by rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase spaces U(N )/U(M )×U(N − M ). Replacing U(N )-spin operators by their expectation values in a Grassmannian coherent state allows for a semi-classical treatment of the low energy U(N )-spin-wave coherent excitations (skyrmions) of U(N ) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.
Current status:
Reports on this Submission
Anonymous Report 1 on 2023-1-23 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202212_00029v1, delivered 2023-01-23, doi: 10.21468/SciPost.Report.6596
Report
In this paper, using group theoretical tools, the authors provides a description of the low energy sector of the Hilbert space of a U(N) quantum Hall/Heisenberg ferromagnet with a certain filling factor. This systems can be phenomenologically achieved and hence their contribution is valuable.
There is a minor error in equation (22), where there is a missed parentheses, which need to be corrected.
Besides this, I recoment this paper for publication in the way that it is.
Author: Manuel Calixto on 2023-01-24 [id 3265]
(in reply to Report 1 on 2023-01-23)We shall add a parentheses inside the bracket of eq. (22) in the final version.
Thank you!
The authors.