Trial wave functions for a Composite Fermi liquid on a torus

TL;DR

This paper develops and tests trial wave functions for a composite Fermi liquid at filling fraction 1/2 on a torus, showing they accurately describe the ground state and excitations, and discusses implications for the nature of composite fermions.

Contribution

It introduces new trial wave functions for a composite Fermi liquid on a torus and demonstrates their accuracy through numerical comparisons with exact diagonalization.

Findings

Trial wave functions accurately describe the ground state and excitations.

The dispersion of composite fermions is characterized.

The Berry phase analysis informs the debate on Dirac nature of composite fermions.

Abstract

We study the two-dimensional electron gas in a magnetic field at filling fraction $\nu=\frac{1}{2}$. At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions.