Topological order in an exactly solvable 3D spin model

Understand

We study a 3D generalization of the toric code model introduced recently by Chamon.

• This is an exactly solvable spin model with six-qubit nearest neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order.
• The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes.
• We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on at least R^2 qubits.