RENORMALIZATION-GROUP CALCULATION FOR ELECTRONS IN A HALF-FILLED LANDAU-LEVEL

The major obstacle for analytic calculations for electrons in the lowe st Landau level arises from the degeneracy of the single-particle eige nstates. When the electron-electron interaction is included, the diago nal energy of different basis states is no longer the same and degener ate perturbation theory can be carried out. The near degeneracy of the single-particle states is manifested as an infrared-divergent perturb ation series which is similar to that of a collection of one-dimension al interacting spinless chains. Thus a renormalization-group scheme ca n be developed. The range of the interparticle potential affects the c hange in diagonal energy for particle-hole fluctuations. For the Coulo mb potential we find that the coupling constants remain unchanged over many length scales. The system remains gapless, consistent with recen t transport and surface-acoustic-wave measurements.