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- Title
The Low-Energy TQFT of the Generalized Double Semion Model.
- Authors
Debray, Arun
- Abstract
The generalized double semion (GDS) model, introduced by Freedman and Hastings, is a lattice system similar to the toric code, with a gapped Hamiltonian whose definition depends on a triangulation of the ambient manifold M, but whose space of ground states does not depend on the triangulation, but only on the underlying manifold. In this paper, we use topological quantum field theory (TQFT) to investigate the low-energy limit of the GDS model. We define and study a functorial TQFT Z GDS in every dimension n such that for every closed (n - 1) -manifold M, Z GDS (M) is isomorphic to the space of ground states of the GDS model on M; the isomorphism can be chosen to intertwine the actions of the mapping class group of M that arise on both sides. Throughout this paper, we compare our constructions and results with their known analogues for the toric code.
- Subjects
HASTINGS (England); TOPOLOGICAL fields; QUANTUM field theory; TORIC varieties; TRIANGULATION; MANIFOLDS (Mathematics); DEFINITIONS
- Publication
Communications in Mathematical Physics, 2020, Vol 375, Issue 2, p1079
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-019-03554-w