A Fermi Fluid Description of the Half-Filled Landau Level

TL;DR

This paper develops a many-body theoretical approach to analyze the ground state properties of electrons at half-filling in a Landau level, employing a simplified trial wave function and plasma analogy.

Contribution

It introduces a novel application of a simplified trial wave function combined with plasma analogy to compute ground state properties at half-filling.

Findings

Pair-correlation function matches expected behavior

Static structure function aligns with theoretical predictions

Ground state energy agrees with known results

Abstract

We present a many-body approach to calculate the ground state properties of a system of electrons in a half-filled Landau level. Our starting point is a simplified version of the recently proposed trial wave function where one includes the antisymmetrization operator to the bosonic Laughlin state. Using the classical plasma analogy, we calculate the pair-correlation function, the static structure function and the ground state energy in the thermodynamic limit. These results are in good agreement with the expected behavior at $\nu=\frac12$.