Ground State Degeneracy in the Levin-Wen Model for Topological Phases

Details Ground State Degeneracy in the Levin-Wen Model for Topological Phases Ground State Degeneracy in the Levin-Wen Model for Topological Phases

2011-05-29

arxiv.org/abs/1105.5771v3

Physics

Condensed Matter

Strongly Correlated Electrons

8 pages, 2 figures. v2: reference added; v3: two appendices added

Scientific paper

We study properties of topological phases by calculating the ground state degeneracy (GSD) of the 2d 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 non-degenerate. 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, consistent with the conjectured equivalence between the LW model associated with a quantum group and the doubled Chern-Simons theory.

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