Multiresolution analysis and fractional quantum Hall effect: more results
Abstract
In a previous paper we have proved that any multiresolution analysis of Script L^{2}(Bbb R) produces, for even values of the inverse filling factor and for a square lattice, a singleelectron 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 nu = 1/3.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 January 2003
 DOI:
 10.1088/03054470/36/1/308
 arXiv:
 arXiv:0904.1111
 Bibcode:
 2003JPhA...36..123B
 Keywords:

 Mathematical Physics
 EPrint:
 J. Phys. A, 36, 123138 (2003)