Occupation Numbers of a Half-Filled Landau Level

TL;DR

This paper compares a recent edge theory of a half-filled Landau level with a variational wave function, showing they predict similar occupation number profiles and matching numerical results.

Contribution

It applies bosonization to Lee and Wen's edge theory, linking it to previous variational approaches and providing analytical expressions for occupation numbers.

Findings

Linear occupation profile in the bulk region

Exponential decay of occupation in the tail region

Good agreement with numerical occupation number data

Abstract

We demonstrate that a theory of the edge of a half-filled Landau level recently proposed by Lee and Wen predicts results for the edge occupation number similar to those of a variational trial wave function proposed previously by us. We treat Lee and Wen's edge action of a half-filled Landau level within the framework of bosonization theory, and show that the momentum occupation numbers are determined by a product of two Green's functions, one charged and one neutral. In the bulk region ($k<0$) we find a linear occupation profile, $n_k \propto A+Bk$, while in the tail region ($k>0$) it is exponentially decaying over the range $k\sim\Ln$, the momentum cutoff for neutral mode. We find a good fit with the numerical results for occupation numbers.