We study the anisotropic effect of the Coulomb interaction on a 1/3-filling
fractional quantum Hall system by using an exact diagonalization method on
small systems in torus geometry. For weak anisotropy the system remains to be
an incompressible quantum liquid, although anisotropy manifests itself in
density correlation functions and excitation spectra. When the strength of
anisotropy increases, we find the system develops a Hall-smectic-like phase
with a one-dimensional charge density wave order and is unstable towards the
one-dimensional crystal in the strong anisotropy limit. In all three phases of
the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of
the anisotropic Coulomb system can be well described by a family of model wave
functions generated by an anisotropic projection Hamiltonian. We discuss the
relevance of the results to the geometrical description of fractional quantum
Hall states proposed by Haldane [ Phys. Rev. Lett. 107 116801 (2011)].Comment: 8 pages, 8 figure
