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Twisted gauge theory model of topological phases in three dimensions

Author(s)
Wan, Yidun; He, Huan; Wang, Juven
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Abstract
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 quasiexcitations 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.
Date issued
2015-07
URI
http://hdl.handle.net/1721.1/97636
Department
Massachusetts Institute of Technology. Department of Physics
Journal
Physical Review B
Publisher
American Physical Society
Citation
Wan, Yidun, Juven C. Wang, and Huan He. "Twisted gauge theory model of topological phases in three dimensions." Phys. Rev. B 92, 045101 (July 2015). © 2015 American Physical Society
Version: Final published version
ISSN
1098-0121
1550-235X

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