Density Matrix Renormalization Group Study of a Lowest Landau Level Electron Gas on a Thin Cylinder

We investigate the ground state properties of a two-dimensional electron gas in the lowest Landau level using the Density Matrix Renormalization Group. The electron gas is confined to a cylinder with a strong magnetic field perpendicular to the surface. For a thin cylinder, the ground state is for generic filling factors a charge density wave state, however, at $\nu=1/2$ a homogeneous and apparently gapless ground state is found and particle and hole excitations are studied.