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Although the adiabatic heuristic argument of the fractional quantum Hallstates has been successful, continuous modification of the flux/statistics ofanyons is strictly prohibited due to algebraic constrains of the braid group ona torus. We have numerically shown that the adiabatic heuristic principle foranyons is still valid even though the Hamiltonians cannot be modifiedcontinuously. The Chern number of the ground state multiplet is the adiabaticinvariant, while the number of the topological degeneracy behaves wildly. Ageneralized Streda formula is proposed that explains the degeneracy pattern.Nambu-Goldston modes associated with the anyon superconductivity are alsosuggested numerically.

Adiabatic Heuristic Principle on a Torus and Generalized Streda Formula