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The generalized double semion (GDS) model, introduced by Freedman andHastings, is a lattice system similar to the toric code, with a gappedHamiltonian whose definition depends on a triangulation of the ambient manifold$M$, but whose space of ground states does not depend on the triangulation, butonly on the underlying manifold. In this paper, we use topological quantumfield theory (TQFT) to investigate the low-energy limit of the GDS model. Wedefine and study a functorial TQFT $Z_{\mathrm{GDS}}$ in every dimension $n$such that for every closed $(n - 1)$-manifold $M$, $Z_{\mathrm{GDS}}(M)$ isisomorphic to the space of ground states of the GDS model on $M$; theisomorphism can be chosen to intertwine the actions of the mapping class groupof $M$ that arise on both sides. Throughout this paper, we compare ourconstructions and results with their known analogues for the toric code.

The low-energy TQFT of the generalized double semion model