Abstract
Simon Trebst (Microsoft Research)
Quantum loop gases and topological order
Two-dimensional quantum loop gases are elementary examples of topological ground states with Abelian or non-Abelian anyonic excitations. In the first part of my talk I will concentrate on the Abelian loop gases, elucidate their stability towards local perturbations such as a small loop tension, and discuss the quantum phase transition into a classically ordered state for large tension. In the second part of the talk, I will show that any microscopic model supporting a gapped non-Abelian quantum loop gas ground state will need non-local interactions. Perturbing a local, gapless Hamiltonian with an anticipated ''non-Abelian'' ground-state wave function immediately drives the system into the Abelian phase.