Bulk and edge correlations in the compressible half-filled quantum Hall state

We study bulk and edge correlations in the compressible half-filled state [B. I. Halperin et al., Phys. Rev. B 47, 7312 (1993) and, E. Rezayi and N. Read, Phys. Rev. Lett. 72, 900 (1994); 73, 1052 (1994)] using a modified version of the plasma analogy. The corresponding plasma has anomalously weak screening properties, and as a consequence, we find that the correlations along the edge do not decay algebraically as in the Laughlin (incompressible) case, while the bulk correlations decay in the same way. The results suggest that due to the strong coupling between charged modes on the edge and the neutral fermions in the bulk, reflected by the weak screening in the plasma analog, the (attractive) correlation hole is not well defined on the edge. Hence, the system there can be modeled as a free Fermi gas of electrons (with an appropriate boundary condition). We finally comment on a possible scenario in which the Laughlin-like dynamical edge correlations may nevertheless be realized.