@misc{10481/75504,
year = {2022},
month = {4},
url = {http://hdl.handle.net/10481/75504},
abstract = {Using the Lieb–Mattis ordering theorem of electronic energy levels, we identify the Hilbert
space of the low energy sector of U(N) quantum Hall/Heisenberg ferromagnets at filling factor M
for L Landau/lattice sites with the carrier space of irreducible representations of U(N) described by
rectangular Young tableaux of M rows and L columns, and associated with Grassmannian phase
spaces U(N)~U(M) × U(N − M). We embed this N-component fermion mixture in Fock space
through a Schwinger–Jordan (boson and fermion) representation of U(N)-spin operators. We provide
different realizations of basis vectors using Young diagrams, Gelfand–Tsetlin patterns and Fock
states (for an electron/flux occupation number in the fermionic/bosonic representation). U(N)-spin
operator matrix elements in the Gelfand–Tsetlin basis are explicitly given. Coherent state excitations
above the ground state are computed and labeled by complex (N −M) ×M matrix points Z on the
Grassmannian phase space. They adopt the form of a U(N) displaced/rotated highest-weight vector,
or a multinomial Bose–Einstein condensate in the flux occupation number representation. Replacing
U(N)-spin operators by their expectation values in a Grassmannian coherent state allows for a
semi-classical treatment of the low energy (long wavelength) U(N)-spin-wave coherent excitations
(skyrmions) of U(N) quantum Hall ferromagnets in terms of Grasmannian nonlinear sigma models.},
organization = {Spanish Government	PGC2018-097831-BI00},
organization = {Junta de Andalucia	SOMM17/6105/UGR	
UHU-1262561	
FQM-381	
FEDER/UJA-1381026},
organization = {Spanish MIU predoctoral fellowship	FPU19/06376},
publisher = {MDPI},
keywords = {N-component fermion mixtures},
keywords = {Quantum Hall ferromagnets},
keywords = {Unitary group representations},
keywords = {Boson Schwinger-Jordan realizations},
keywords = {Young tableaux},
keywords = {Lieb-Mattis theorem},
keywords = {Grassmannian sigma models},
title = {Hilbert Space Structure of the Low Energy Sector of U(N) Quantum Hall Ferromagnets and Their Classical Limit},
doi = {10.3390/sym14050872},
author = {Calixto Molina, Manuel and Mayorgas Reyes, Alberto and Guerrero, Julio},
}