Abstract
We propose an exactly solvable lattice Hamiltonian model of topological phases in dimensions, based on a generic finite group and a 4-cocycle over . 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 generators as the modular and matrices of the ground states, which yield a set of topological quantum numbers classified by and quantities derived from . Our model fulfills a Hamiltonian extension of the -dimensional Dijkgraaf-Witten topological gauge theory with a gauge group . This work is presented to be accessible for a wide range of physicists and mathematicians.
2 More- Received 9 October 2014
- Revised 28 May 2015
DOI:https://doi.org/10.1103/PhysRevB.92.045101
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