2014/09/30 by Yidun Wan, Juven Wang, Huan He · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.str-el #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevb.92.045101
published as Phys. Rev. B 92, 045101 (2015) · 37 pages, 9 figures, 4 tables; revised to improve the clarity; references added
arxiv created 2014/10/08 · arxiv updated 2015/07/02
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.