Anisotropy in the compressible quantum Hall state

Using a mean field theory on the von Neumann lattice, we study compressible anisotropic states around v = l + 1/2 in the quantum Hall system. The Hartree-Fock energy of the unidirectional charge density wave (UCDW) are calculated self-consistently. In these states the UCDW seems to be the most plausible state. We show that the UCDW is regarded as a collection of the one-dimensional lattice fermion systems which extend to the uniform direction. The kinetic energy of this one-dimensional system is induced from the Coulomb interaction term and the self-consistent Fermi surface is obtained.