Quantum 2-Body Hamiltonian for Topological Color Codes

Details Quantum 2-Body Hamiltonian for Topological Color Codes Quantum 2-Body Hamiltonian for Topological Color Codes

2009-07-06

arxiv.org/abs/0907.0948v1

Fortsch.Phys.57:1103-1110,2010

Physics

Quantum Physics

Cotribution to the Proceedings of the Scala Conference 2009 (Cortina, Italy). Special Issue dedicated to Prof. Prof. Tombesi,

Scientific paper

10.1002/prop.200900084

We introduce a two-body quantum Hamiltonian model with spins-$\half$ located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non-perturbative effect. The model has a $\Z_2\times \Z_2$ gauge group symmetry and string-net integrals of motion. There exists a gapped phase in which the low-energy sector reproduces an effective topological color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. All these, and more, are new features not present in honeycomb lattice models like Kitaev model.

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