Trial wave functions for a composite Fermi liquid on a torus

Fractional quantum Hall effect fluids remain the prototype systems with topological order and strong interactions. They are usually well described as integer quantum Hall states of composite fermions, made of electrons and magnetic flux quanta. The authors investigate a two-dimensional electron gas in a magnetic field at half filling. This system should be described by a Fermi liquid of composite fermions in zero field and is uniquely suited to study the nature of composite fermions as, for instance, to determine if they are Dirac fermions. The composite Fermi liquid is indeed found to give an excellent approximation of the low-energy physics. It also shows unexpected features in the Berry curvature of the composite fermions.