Skyrmions without Sigma Models in Quantum Hall Ferromagnets

We report on a microscopic theory of the Skyrmion states that occur in the quantum Hall regime. The theory is based on the identification of Skyrmion states in this system with zero-energy eigenstates of a hard-core model Hamiltonian. We find that for $N_{\phi }$ orbital states in a Landau level, a set of Skyrmion states with orbital degeneracy $N_{\phi }-K$ and spin quantum number $S=N/2-K$ exists for each non-negative integer $K$. The energetic ordering of states with different $K$ depends on the interaction potential.