Bulk and edge excitations of aν=1Hall ferromagnet

Abstract

We focus on the collective dynamics of the fermions in a $\ensuremath{\nu}=1$ quantum-Hall droplet. Specifically, we look at the quantum Hall ferromagnet. In this system, the electron spins are ordered in the ground state due to the exchange part of the Coulomb interaction and the Pauli exclusion principle. The low-energy excitations are ferromagnetic magnons. In order to obtain an effective Lagrangian for these magnons, we introduce bosonic collective coordinates in the Hilbert space of many-fermion systems. These collective coordinates describe a part of the fermionic Hilbert space. Using this technique, we interpret the magnons as bosonic collective excitations in the Hilbert space of the many-electron Hall system. Furthermore, by considering a Hall droplet of finite extent, we also obtain the effective Lagrangian governing the spin collective excitations at the edge of the sample.