TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysProc.14.021
TI  - Hilbert space structure and classical limit of the low energy sector of U(N) quantum Hall ferromagnets
PY  - 2023/11/23
UR  - https://www.scipost.org/SciPostPhysProc.14.021
JF  - SciPost Physics Proceedings
JA  - SciPost Phys. Proc.
VL  - 
IS  - 14
SP  - 021
A1  - Calixto, Manuel
AU  - Mayorgas, Alberto
AU  - Guerrero, Julio
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysProc.14.021,
	title={{Hilbert space structure and classical limit of the low energy sector of U(N) quantum Hall ferromagnets}},
	author={Manuel Calixto and Alberto Mayorgas and  Julio Guerrero},
	journal={SciPost Phys. Proc.},
	pages={021},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysProc.14.021},
	url={https://scipost.org/10.21468/SciPostPhysProc.14.021},
}