St. Chui, RENORMALIZATION-GROUP CALCULATION FOR ELECTRONS IN A HALF-FILLED LANDAU-LEVEL, Physical review. B, Condensed matter, 48(23), 1993, pp. 17343-17349
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.