Topological solitons in Chern-Simons theories for the double-layer fractional quantum Hall effect

Topological excitations in Chern-Simons (CS) gauge theories which describe the double-layer fractional quantum Hall effect are studied. We shall consider the generic ( m, m, n) Halperin state. There are two types of solitons; one is the vortex type excitation which has essentially the same structure with the quasi-hole excitation in the single-layer case. The other is the non-trivial pseudospin texture which is the so-called skyrmion or meron. We shall first study qualitative properties of solitons in the original CS gauge theory and give results of numerical calculations. Then, by using a duality transformation, we derive an effective theory for topological excitations in the fractional quantum Hall effect. For spin texture, that theory is the non-relativistic CP ¹ non-linear σ-model with a CS gauge interaction and a Hopf term. Finally, we study a quantum mechanical system of multi-soliton states, retaining only the center coordinates of solitons as collective coordinates. The existence of inter-layer tunneling drastically changes the excitation spectrum.