Hilbert Space Structure of the Low Energy Sector of U(N) Quantum Hall Ferromagnets and Their Classical Limit Calixto Molina, Manuel Mayorgas Reyes, Alberto Guerrero, Julio N-component fermion mixtures Quantum Hall ferromagnets Unitary group representations Boson Schwinger-Jordan realizations Young tableaux Lieb-Mattis theorem Grassmannian sigma models 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. 2022-06-15T09:07:59Z 2022-06-15T09:07:59Z 2022-04-24 journal article Calixto, M.; Mayorgas, A.; Guerrero, J. Hilbert Space Structure of the Low Energy Sector of U(N) Quantum Hall Ferromagnets and Their Classical Limit. Symmetry 2022, 14, 872. [https://doi.org/10.3390/sym14050872] http://hdl.handle.net/10481/75504 10.3390/sym14050872 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España MDPI