Anisotropy in the Compressible Quantum Hall State

Using a mean field theory on the von Neumann lattice, we study compressible anisotropic states around $\nu =l+1\mathrm{/}2$ in the quantum Hall system. The Hartree-Fock energy of the UCDW are calculated self-consistently. In these states the unidirectional charge density wave (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.