Composite-fermion Fermi surface at the half-filled Landau level with 2n-fold rotational symmetry

The nature of the composite-fermi liquid state that occurs at the half-filled Landau level remains an exciting problem in the theory of quantum Hall effect. In this work, we look at its response to anisotropic electron-electron interactions of various types with 2n-fold rotational symmetry. Using the infinite-cylinder density matrix renormalization group (iDMRG) method, we determine the shape of the composite-fermion (CF) Fermi surface and study the amount of anisotropy transferred from the interactions. We find that for n>1, CFs respond very weakly to the anisotropy for the case of Coulomb (~ 1/r) interactions. Our results shed light on the relation between the CF effective mass tensor and electron-electron interactions.