Resonating-valence-bond physics and topological order in two dimensions: from dimer models to high-temperature superconductivity

The notion of Z(2) topological order in two-dimensional resonating-valence-bond systems is reviewed. Using quantum dimer models as an example, I discuss general properties of the topological order and the resulting vortex-like excitations (visons). Some connections to theories of frustrated magnetism and of high-temperature superconductivity are pointed out.