# Exact topological quantum order in D=3 and beyond : Branyons and brane-net condensates

@article{Bombin2007ExactTQ,
title={Exact topological quantum order in D=3 and beyond : Branyons and brane-net condensates},
author={H. Bombin and Miguel Angel Martin-Delgado},
journal={Physical Review B},
year={2007},
volume={75},
pages={075103}
}
• Published 27 July 2006
• Physics
• Physical Review B
We construct an exactly solvable Hamiltonian acting on a 3-dimensional lattice of spin-$\frac 1 2$ systems that exhibits topological quantum order. The ground state is a string-net and a membrane-net condensate. Excitations appear in the form of quasiparticles and fluxes, as the boundaries of strings and membranes, respectively. The degeneracy of the ground state depends upon the homology of the 3-manifold. We generalize the system to $D\geq 4$, were different topological phases may occur. The… Expand
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