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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 · Alberto Mayorgas
Submission information
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
  • Condensed Matter Physics - Theory
  • Mathematical Physics
  • Quantum Physics
Approach: Theoretical


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.

Published as SciPost Phys. Proc. 14, 021 (2023)

Author comments upon resubmission

Dear Editor,

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.


Manuel Calixto
University of Granada

List of changes

We have added a missing parenthesis to formula 22.

Submission & Refereeing History

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Resubmission scipost_202212_00029v2 on 15 February 2023

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