Teil eines Buches,
Mapping interacting onto non-interacting quantum Hall systems
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Zusammenfassung
We construct an explicit duality between the interacting quantum Hall system in the lowest Landau level and a non-interacting Landau problem. This is done by absorbing the interaction into the gauge field in the form of an effective magnetic vector potential. The result is analogous to, and illuminates the microscopic origin of, the well-known composite fermion model, but has several advantageous properties. In particular, the gaps exhibit the correct scaling behaviour and the origin of the robustness of incompressibility with respect to changes in the interaction is made clear. Using this duality we derive, for an arbitrary short-range interaction, analytic expressions for the ground state energy and the excitation gap as functions of the filling fraction. We find very good agreement with existing numerical results. Performing an analogous construction in the path-integral formalism produces the familiar Chern-Simons field theory description, and we will outline this approach briefly.
