TOPOLOGICAL SOLITONS IN CHERN-SIMONS THEORIES FOR THE DOUBLE-LAYER FRACTIONAL QUANTUM HALL-EFFECT

Topological excitations in Chem-Simons (CS) gauge theories which descr ibe the double-layer fractional quantum Hall effect are studied, We sh all consider the generic (m, m, m) 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 numeri cal calculations. Then, by using a duality transformation, we derive a n effective theory for topological excitations in the fractional quant um Hall effect, For spin texture, that theory is the non-relativistic CP1 non-linear sigma-model with a CS gauge interaction and a Hopf term . Finally, we study a quantum mechanical system of multi-soliton state s, retaining only the center coordinates of solitons as collective coo rdinates. The existence of inter-layer tunneling drastically changes t he excitation spectrum. (C) 1997 Elsevier Science B.V.