Intrinsic edge dipole moment of incompressible fractional quantum Hall ground states

The edges of incompressible fractional quantum Hall (FQH) fluids have a characteristic dipole moment related to their Hall viscosity, which can be split into two separate contributions: a (trivial) contribution from the Landau orbit (common to all FQH fluids in the same Landau level, and a (non-trivial) guiding-center contribution that depends on the FQH state. Using the model wave functions for (fermonic and bosonic) Laughlin states ($\nu$ = 1/2, 1/3, 1/4), and Moore-Read states ($\nu$ = 2/2, 2/4) expressed as Jack polynomials, we obtained the guiding-center occupation number distributions $n(k)$ of ``Landau-gauge" basis states with $k$ near the edge $``\nu^{-1}k_F"$ of a FQH fluid in cylindrical geometries of various circumferences, and verified the ``Luttinger" and ``edge-dipole" sum rule. The edge-dipole moments of the FQH fluids were expressed as a combination of quantized quantities: electric charge e, ``guiding center spin" s and number of fluxes per ``composite boson'' q in [F. D. M. Haldane, arXiv:0906.1854 (2009)]. Our work provides a numerical verification of the prediction. The edge dipole experiences a force due to the gradient of electric field perpendicular to the edge, and the force is balanced by stress from the ``guiding center Hall viscosity".