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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, 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_00029v2 (pdf) |
| Date accepted: | 2023-08-11 |
| Date submitted: | 2023-02-15 11:06 |
| 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.
Author comments upon resubmission
Please find enclosed the revised version of the paper "Hilbert Space Structure and Classical Limit of the Low Energy Sector of U(N) Quantum Hall Ferromagnets" by Alberto Mayorgas, Julio Guerrero and myself, which is submitted to SciPost Physics Proceedings for publication.
Sincerely,
Manuel Calixto
calixto@ugr.es
University of Granada
Spain
List of changes
We have added a missing parenthesis to formula 22.
Published as SciPost Phys. Proc. 14, 021 (2023)