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

Neutral excitation and bulk gap of the Fractional Quantum Hall liquids in disk geometry