Schedule Nov 09, 2005
Anyons in an Exactly Solved Model and Beyond
Dr. Alexei Kitaev, KITP & Microsoft

I will describe a particular spin model on a two-dimensional lattice, which exhibits topological order, chiral edge states, "weak symmetry breaking" and other interesting properties, providing a lot of insight into the general nature of these phenomena. The Hamiltonian can be diagonalized exactly by a reduction to free fermions in a static $Z_2$ gauge field. The system has two phases, one of which is gapped and carries Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field, in which case excitations are non-Abelian anyons. I will also discuss a general theory of free fermions with a gapped spectrum characterized by a spectral Chern number $\nu$. The Abelian and non-Abelian phases of the original model correspond to $\nu=0$ and $\nu=\pm 1$, respectively. The anyonic properties of excitation depend on $\nu\bmod 16$, whereas $\nu$ itself governs edge thermal transport.
See cond-mat/0506438

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