Interactions and disorder in topological quantum matter

Simon Trebst, University of Cologne

The emergence of topological order is one of the most intriguing phenomena in quantum many-body physics and one of possibly far reaching relevance -- topological quantum matter is increasingly appreciated as possible medium for quantum computation purposes.

In this talk I will give a short overview of the formation of topological quantum matter in a variety of physical systems -- both from an experimental and a more conceptual point of view.

The stability of topological order against local perturbations is one of its defining characteristics, which I will discuss in regard to actual experimental settings and in light of theoretical proposals to build a topological quantum computer. Our own interest in this realm has focused on the effects of interactions and disorder on the collective quantum state formed by a set of topological excitations, so- called anyons. One of the possible instabilities -- the formation of a thermal metal state -- leads to the somewhat counterintuitive conclusion that in order to make a quantum computer work a little heat could actually help.