For the fast rotating quasi-two-dimensional dipolar fermions in the quantum Hall regime, the interaction between two dipoles breaks the rotational symmetry when the dipole moment has in-plane components that can be tuned by an external field. Assuming that all the dipoles are polarized in the same direction, we perform the numerical diagonalization for finite size systems on a torus. We find that while ν = 1/3 Laughlin state is stable in the lowest Landau level (LLL), it is not stable in the first Landau level (1LL); instead, the most stable Laughlin state in the 1LL is the ν = 2 + 1/5 Laughlin state. These FQH states are robust against moderate introduction of anisotropy, but large anisotropy induces a transition into a compressible phase in which all the particles are attracted and form a bound state. We show that such phase transitions can be detected by the intrinsic geometrical properties of the ground states alone. The anisotropy and the phase transition are systematically studied with the generalized pseudopotentials and characterized by the intrinsic metric, the wave function overlap and the nematic order parameter. We also propose simple model Hamiltonians for this physical system in the LLL and 1LL respectively.

For the numerical simulation of the fractional quantum Hall effects on a finite disk, the rotational symmetry is the only symmetry that were used in diagonalizing the Hamiltonian. In this work, we propose a method of using the weak translational symmetry for the center of mass of the many-body system. With this approach, the bulk properties , such as the energy gap and the magneto-roton excitation are exactly consistent with that in the closed manifold like sphere and torus. As an application, we consider the FQH phase and its phase transition in the fast rotated dipolar fermions. We thus weapon the disk geometry versatility in analyzing the bulk properties beside the usual edge physics.