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Topological Order: Phases of Matter with Fascinating Properties

Einladung zum Physikalischen Kolloquium im Wintersemester 2016/17

Condensed matter is found in a variety of phases, the vast majority of which are characterized in
terms of symmetry breaking. For example, magnets spontaneously break time-reversal and spinrotation symmetries.

A notable exception was provided by the discovery of the quantum Hall effects which exhibit new
kinds of topological orders not associated with any symmetry breaking. One of the characterizing
features of topological order is the existence of excitations with exotic properties. These so-called
anyonic excitations might make topologically ordered systems ideal building blocks of faulttolerant
quantum computers. In this colloquium, I will start by giving a general introduction to the
concept of topological order and then address some of the recent developments. In particular, I
will introduce theoretical frameworks that allow us to classify topological phases and discuss
dynamical signatures that are useful to experimentally detect them.