Twisted Gauge Theory Model of Topological Phases in Three Dimensions

Yidun Wan Juven Wang Huan He

Mathematical Physics Theoretical Physics mathscidoc:1904.22006

Phys. Rev., 2015
We propose an exactly solvable lattice Hamiltonian model of topological phases in 3+1 dimensions, based on a generic finite group G and a 4-cocycle ω over G. We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the 3-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasi-excitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the SL(3,Z) generators as the modular S and T matrices of the ground states, which yield a set of topological quantum numbers classified by ω and quantities derived from ω. Our model fulfills a Hamiltonian extension of the 3+1-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group G. This work is presented to be accessible for a wide range of physicists and mathematicians.
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  title={Twisted Gauge Theory Model of Topological Phases in Three Dimensions},
  author={Yidun Wan, Juven Wang, and Huan He},
  booktitle={Phys. Rev.},
Yidun Wan, Juven Wang, and Huan He. Twisted Gauge Theory Model of Topological Phases in Three Dimensions. 2015. In Phys. Rev..
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