Topological order is an unconventional way of quantum organization that contradicts the traditional paradigms of condensed matter physics. Topological states of matter obey emergent global rules, which are dramatically different from the fundamental laws governing the microscopic individuals. For instance, a system of bosonic or fermionic particles forming a topological state can generate excitations that are neither bosons nor fermions, but anyons with novel braiding statistics. In this lecture I will explain the concepts of topological order and anyons, exploring seminal examples, like fractional quantum Hall systems and quantum loop models.
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