The edge theory of ferromagnetic quantum Hall states

Abstract

We propose an effective low-energy theory for ferromagnetic Hall states. It describes the charge degrees of freedom, on the edge, by a (1 + 1) dimensional chiral boson theory, and the spin degrees of freedom by the (2 + 1)dimensional quantum ferromagnet theory in the spin-wave approximation. The usual chiral boson theory for spinless electrons is modified to include the charge degrees of freedom with spin. Our total, bulk plus edge, effective action is gauge invariant and we find a generalized "chiral anomaly" in this case. We describe two, charged and neutral, sets of edge spin-wave solutions. The spreading of these waves is much larger than the one for the charge (edge) waves and they have linear dispersion relations.