Persisting topological order via geometric frustration
Dr. Kai Schmidt (TU Dortmund)

Correlated quantum systems in two dimensions display a variety of fascinating properties. One of the most intriguing issues is the concept of topological order which goes beyond the paradigm of classifying the ground states of nature by spontaneous symmetry breaking. Topologically-ordered quantum systems possess elementary excitations with fractional quantum numbers and unconventional particle statistics. One of the standard models displaying topological order is the so-called toric code which is an exactly solvable model of interacting spins.

In this talk we study the stability of the topological phase in the toric code model in the presence of a uniform magnetic field. Furthermore, we introduce a toric code on the dice lattice which is also exactly solvable and topologically ordered at zero temperature. In the presence of a magnetic field, the flux dynamics is mapped to the highly frustrated transverse field Ising model on the kagome lattice. This correspondence suggests an intriguing disorder by disorder phenomenon in a topologically ordered system implying that the topological order is extremely robust due to the geometric frustration. A general connection between fully frustrated transverse field Ising models and topologically ordered systems is demonstrated.