Numerical study of anisotropy in a composite Fermi liquid

We perform density-matrix renormalization group studies of a two-dimensional electron gas in a high perpendicular magnetic field and with an anisotropic band mass. At half filling in the lowest Landau level, such a system is a Fermi liquid of composite fermions. By measuring the Fermi surface of these composite fermions, we determine a relationship between the anisotropy of composite fermion dispersion αCF and the original anisotropy αF of the fermion dispersion at zero magnetic field. For systems where the electrons interact via a Coulomb interaction, we find αCF=αF within our numerical accuracy. The same result has been found concurrently in recent experiments. We also find that the relationship between the anisotropies is dependent on the form of the electron-electron interaction.