Skyrmions without Sigma Models in Quantum Hall Ferromagnets

TL;DR

This paper develops a microscopic theory for Skyrmion states in quantum Hall ferromagnets, linking them to zero-energy eigenstates of a specific Hamiltonian, and explores their degeneracy and energy ordering.

Contribution

It introduces a novel microscopic framework identifying Skyrmion states with zero-energy eigenstates, bypassing sigma models, and characterizes their degeneracy and energy hierarchy.

Findings

Skyrmion states correspond to zero-energy eigenstates of a hard-core Hamiltonian.

For each nonnegative integer K, a set of Skyrmion states with specific degeneracy and spin exists.

The energy ordering of Skyrmion states depends on the interaction potential.

Abstract

We report on a microscopic theory of the Skyrmion states which 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 Skyrmions states with orbital degeneracy $N_{\phi}-K$ and spin quantum number $S = N/2 -K$ exists for each nonnegative integer $K$. The energetic ordering of states with different $K$ depends on the interaction potential.