Twisted quantum double model of topological phases in two dimensions

By Yuting Hu, Yidun Wan, Yong-Shi Wu. 2012

153 citations recorded by the source corpus.

We propose a new discrete model—the twisted quantum double model—of 2D topological phases based on a finite group G and a 3-cocycleover G. The detailed properties of the ground states are studied, and we find that the ground-state subspace can be characterized in terms of the twisted quantum double D � (G) of G. Whenis the trivial 3-cocycle, the model becomes Kitaev's quantum double model based on the finite group G, in which the elementary excitations are known to be classified by the quantum double D(G) of G. Our model can be viewed as a Hamiltonian extension of the Dijkgraaf-Witten topological gauge theories to the discrete graph case with gauge group being a finite group. We also demonstrate a duality between a large class of Levin-Wen string-net models and certain twisted quantum double models, by mapping the string-net 6j symbols to the corresponding 3-cocycles. The paper is presented in a way such that it is accessible to a wide range of physicists.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/e37cef0393a843e2a94042dbe4853fa5da3f7602

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward (2022, unknown): “The resulting state will be a twisted quantum double of G [90, 91].”
Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, background): “Third, it allows for the preparation of states that are not realized by stabilizer codes, such as topological order described by twisted gauge theories or non-Abelian fracton orders [60– 69].”
Measurement as a Shortcut to Long-Range Entangled Quantum Matter (2022, background): “Double semion – An interesting application is the constant-depth preparation of a twisted Z2 topological order [39], i.”
Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions (2017, unknown): “[57, 58].”
Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions (2016, background): “(3) is suitable for topological order that has its Hilbert space and group elements associated to the links on a spatial lattice [18, 19, 22], whereas its group cohomology implementing the inhomogeneous cocycle and its holonomies are non-trivial for cycles of closed manifold thus |Z| sums over diffe”