Abstract:
Non-abelian anyons are candidates for decoherence-free qubits in fault-tolerant topological quantum computation. A simple and explicit expression of non-abelian anyons with experimental achievable quantities is essential to design such a quantum computer. Towards this expression, we first illustrate the vortex solutions with real space spin configurations in a tetrahedron spin model. These vortices are exact eigen states of this small spin lattice model and obey non-abelian fusion rules. To substantiate the nonabelian anyons, we generalize the single tetrahedron model to a chain model of tetrahedrons on a torus. We find that the non-abelian vortices may be regarded as well-defined non-abelian anyons. Since these anyons are exhibited by real space spin configurations, they can be realized by means of recently developed experimental techniques. The explicit expression of the non-abelian fusion rules also gives an intuitional picture to these abstract field theoretical contexts.
Coffee and tea will be served 20 minutes prior to the seminar.