Multi-resolution analysis and fractional quantum hall effect: More results

Abstract

In a previous paper we have proved that any multi-resolution analysis of ℒ2(ℝ) produces, for even values of the inverse filling factor and for a square lattice, a single-electron wavefunction of the lowest Landau level (LLL) which, together with its (magnetic) translate, gives rise to an orthonormal set in the LLL. We have also discussed the inverse construction. In this paper we simplify the procedure, clarifying the role of the kqrepresentation. Moreover, we extend our previous results to the more physically relevant case of a triangular lattice and to odd values of the inverse filling factor. We also comment on other possible shapes of the lattice as well as on the extension to other Landau levels. Finally, just as a first application of our technique, we compute (an approximation of) the Coulomb energy for the Haar wavefunction, for a filling v = 1/3.