Geometry and String Theory Seminar, 02 September 2015
Valentin Zakharevich, UT Austin, Mathematics
Kitaev's Toric Code
abstract
Kitaev's toric code is a hamiltonian model with an energy gap whose low energy theory reproduces Dijkgraaf-Witten TQFT in 2+1 dimensions. Having these TQFT's as the low energy topological theory implies degeneracy of the ground state of the system depending on topology of the space manifold as well as existence of quasi-particle excitations with non-trivial braiding statistics. In this talk we will observe these phenomena explicitly.