2008/04/30 by G. Kells, Graham Kells, Ahmet Tuna Bolukbasi +8 · 48 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Annihilation #Degeneracy (biology) #Fermion #Geometry #Hamiltonian (control theory) #Homogeneous space #Lattice (music) #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Symmetry protected topological order #Theoretical physics #Topological defect #Topological degeneracy #Topological order #Topology (electrical circuits) #Vortex #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevlett.101.240404
published in Physical Review Letters 101(24), 240404 (American Physical Society) · 4 pages, 3 figures, Revised version, accepted to PRL
arxiv created 2008/11/11 · openalex publication_date 2008/12/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite size effects and note that in the thermodynamic limit it is robust to all orders. Further, we demonstrate that the loop symmetries themselves correspond to the creation, propagation, and annihilation of fermions. We note that these fermions, made from pairs of vortices, can be moved with no additional energy cost.