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

TL;DR

This paper investigates the ground state degeneracy in the Levin-Wen model for topological phases, demonstrating its dependence on topology, non-degeneracy on a sphere, and correspondence with doubled Chern-Simons theory on a torus.

Contribution

It explicitly shows the GSD depends only on topology and confirms the equivalence between the Levin-Wen model with quantum groups and doubled Chern-Simons theory.

Findings

GSD depends solely on spatial topology

Ground state on a sphere is always non-degenerate

GSD on a torus matches doubled Chern-Simons theory

Abstract

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.