| We study quantum Hall ferromagnets with a finite density of topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrised by a d-component complex spinor field. We first consider a fully SU(d) symmetric model, that differs from the usual CP(d-1) model by the long ranged Coulomb interaction. This additional term lifts the massive ground-state degeneracy present in the short range CP(d-1) model, and selects a hexagonal Skyrmion lattice which spontaneously breaks the underlying SU(d) symmetry. The ground state charge density modulation, which inevitably exists in these lattices, vanishes exponentially in d. We compute analytically the complete low-lying excitation spectrum, which separates into d2-1 gapless acoustic magnetic modes and a magnetophonon. We discuss the role of effective mass anisotropy for SU(3)-valley Skyrmions relevant for experiments with AlAs quantum wells. Here, we find a transition, which breaks a six-fold rotational symmetry of a triangular lattice, appearing at weak anisotropy, followed by a formation of a square lattice at large values of anisotropy strength. |
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