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

TL;DR

This paper investigates the unique correlation behaviors in the compressible half-filled quantum Hall state, revealing weak edge screening and a transition to free Fermi gas behavior at the edge, contrasting with the Laughlin state.

Contribution

It introduces a modified plasma analogy to analyze bulk and edge correlations, uncovering weak screening effects and edge behavior distinct from incompressible quantum Hall states.

Findings

Edge correlations do not decay algebraically, unlike in Laughlin states.

Bulk correlations decay similarly to Laughlin states.

Edge can be modeled as a free Fermi gas of electrons.

Abstract

We study bulk and edge correlations in the compressible half-filled state, 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 analogue, the (attractive) correlation hole is not well defined on the edge. Hence, the system there can be modeled as a free Fermi gas of {\em 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.