Twisted gauge theory model of topological phases in three dimensions

Yidun Wan, Juven C. Wang, and Huan He
Phys. Rev. B 92, 045101 – Published 1 July 2015

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.

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  • Received 9 October 2014
  • Revised 28 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.045101

©2015 American Physical Society

Authors & Affiliations

Yidun Wan1,*, Juven C. Wang1,2,†, and Huan He1,3,‡

  • 1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
  • 2Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 3Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

  • *ywan@perimeterinstitute.ca
  • juven@mit.edu
  • huanh@princeton.edu

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Vol. 92, Iss. 4 — 15 July 2015

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