Loop Condensation in Quantum Dimer Models
Topologically ordered phases of matter are quantum liquids with a non-local quantum order. Because of their unique properties due to the non-local quantum entanglement present in these phases, topological phases have been proposed as the basis of a physically fault-tolerant quantum computer. The formation of such topological order is well understood in terms of the mechanism of loop condensation in systems with loop-like degrees of freedom. Certain quantum dimer models posses topologically ordered dimer liquid ground states and can be mapped to loop models. In this dissertation we present a study of the geometric properties of the loop condensates of quantum dimer models and related models using classical Monte Carlo as well as ground state quantum Monte Carlo calculations. Additionally, we present an approach for the robust experimental generation of a topologically ordered phase in a system of neutral atoms trapped in an optical lattice.