Adiabatic Heuristic Principle on a Torus and Generalized Streda Formula

Abstract

Although the adiabatic heuristic argument of the fractional quantum Hall states has been successful, continuous modification of the flux/statistics of anyons is strictly prohibited due to algebraic constrains of the braid group on a torus. We have numerically shown that the adiabatic heuristic principle for anyons is still valid even though the Hamiltonians cannot be modified continuously. The Chern number of the ground state multiplet is the adiabatic invariant, while the number of the topological degeneracy behaves wildly. A generalized Streda formula is proposed that explains the degeneracy pattern. Nambu-Goldston modes associated with the anyon superconductivity are also suggested numerically.

arXiv comment7 pages

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Cited by in corpus (7)

• Kohn-Sham Density Functional Theory of Abelian Anyons
• Composite anyons on a torus
• Bulk-edge Correspondence in the Adiabatic Heuristic Principle
• Adiabatic Continuity of the Spinful Quantum Hall States
• Superconductivity in a system of interacting spinful semions
• Candidate local parent Hamiltonian for 3/7 fractional quantum Hall effect
• Crossover from Integer to Fractional Quantum Hall Effect