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

## TL;DR

This paper introduces a method leveraging weak translational symmetry in disk geometry to accurately analyze bulk properties like energy gaps and excitations in fractional quantum Hall systems, aligning with results from closed geometries.

## Contribution

It proposes a novel approach using weak translational symmetry for finite disk simulations, improving the analysis of bulk properties in fractional quantum Hall liquids.

## Key findings

- Bulk energy gap matches sphere and torus results
- Magneto-roton excitation spectrum is consistent with closed geometries
- Method enables versatile bulk property analysis in disk geometry

## Abstract

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.