Half-Filled Lowest Landau Level on a Thin Torus

TL;DR

This paper models a half-filled Landau level on a thin torus, revealing a one-dimensional neutral fermion system with gapless excitations, resembling the bulk composite fermion state and suggesting a Luttinger liquid description.

Contribution

It provides an exact solution for the half-filled Landau level on a thin torus, connecting it to the bulk composite fermion state and proposing a one-dimensional Luttinger liquid framework.

Findings

Ground state is a homogeneous Fermi sea of neutral fermions.

Excitations are gapless neutral modes.

Resembles the bulk $ u=1/2$ composite fermion state.

Abstract

We solve a model that describes an interacting electron gas in the half-filled lowest Landau level on a thin torus, with radius of the order of the magnetic length. The low energy sector consists of non-interacting, one-dimensional, neutral fermions. The ground state, which is homogeneous, is the Fermi sea obtained by filling the negative energy states and the excited states are gapless neutral excitations out of this one-dimensional sea. Although the limit considered is extreme, the solution has a striking resemblance to the composite fermion description of the bulk $\nu=1/2$ state--the ground state is homogeneous and the excitations are neutral and gapless. This suggests a one-dimensional Luttinger liquid description, with possible observable effects in transport experiments, of the bulk state where it develops continuously from the state on a thin torus as the radius increases.