Microscopic study of the composite Fermi liquid

We use exact diagonalization (ED) to study a many-body generalization of the $k$-space Berry phase for taking a quasiparticle around the Fermi surface of a $\nu=1/2$ composite Fermi liquid (CFL). Composite fermion ``occupations'' are identified by a large overlap between the ED state and an explicit model CFL wavefunction. This model wavefunction is found to be very accurate, and also nearly particle-hole symmetric, when the composite fermion quasiparticles are clustered to form a compact Fermi sea. For a sequence of occupation configurations where excitations stay close to the Fermi surface, we find a net phase of $\pi$, consistent with an anomalous Hall effect with $\sigma^{xy}=1/2 (e^2/h)$ and with a recent Dirac fermion effective theory.