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

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions