2011/05/31 by Yuting Hu, Spencer D. Stirling, Yong-Shi Wu
Mathematics · Physics and Astronomy · #Combinatorics #Degeneracy (biology) #Degenerate energy levels #Equivalence (formal languages) #Geometry #Ground state #Group (periodic table) #Mathematics #Physics #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Symmetry protected topological order #Theoretical physics #Topological Materials and Phenomena #Topological degeneracy #Topological order #Topology (electrical circuits) #Torus #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.85.075107
8 pages, 2 figures. v2: reference added; v3: two appendices added
arxiv created 2012/01/20 · openalex publication_date 2012/02/07 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the properties of topological phases by calculating the ground-state degeneracy (GSD) of the two-dimensional Levin-Wen (LW) model. Here it is explicitly shown that the GSD depends only on the spatial topology of the system. Then we show that the ground state on a sphere is always nondegenerate. Moreover, we study an example associated with a quantum group, and show that the GSD on a torus agrees with that of the doubled Chern-Simons theory, which is consistent with the conjectured equivalence between the LW model associated with a quantum group and the doubled Chern-Simons theory.