The Quantum Hall System in a Solvable Limit

Anders Karlhede

Stockholm University, Sweden

We consider spin-polarized interacting electrons in the lowest Landau level. We solve the problem exactly, for arbitrary filling factor, on a thin torus and show that the states with odd denominators can be organized in a fractional pattern consistent with the Haldane-Halperin hierarchy and with a global phase diagram proposed earlier. The exact solutions have the same qualitative properties as the bulk quantum Hall states and are continuous limits of the wave functions that describe these states. For the half-filled Landau level an exact solution in terms of non-interacting dipoles is obtained. The analysis in the solvable limit is extended to non-abelian states, such as the Moore-Read state, where the non-trivial degeneracies of the excitations are obtained.