Renormalization-group calculation for electrons in a half-filled Landau level.

Abstract

The major obstacle for analytic calculations for electrons in the lowest Landau level arises from the degeneracy of the single-particle eigenstates. When the electron-electron interaction is included, the diagonal energy of different basis states is no longer the same and degenerate perturbation theory can be carried out. The near degeneracy of the single-particle states is manifested as an infrared-divergent perturbation series which is similar to that of a collection of one-dimensional interacting spinless chains. Thus a renormalization-group scheme can be developed. The range of the interparticle potential affects the change in diagonal energy for particle-hole fluctuations. For the Coulomb potential we find that the coupling constants remain unchanged over many length scales. The system remains gapless, consistent with recent transport and surface-acoustic-wave measurements.