Strange and subtle states of matter – the topological ideas behind the 2016 Nobel Prize in Physics
Goldbart, Paul M.
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The gases, liquids, and solids that humans have known and harnessed since prehistory are human-scale reflections of how atoms and molecules are organized at the atomic scale. This organization is driven by the forces exerted by atoms and molecules on one another. At high temperatures, the organization consists only of local conspiracies that continually form and decay but are too small to have much impact. At low temperatures, however, the conspiracies spread to become global revolutions, which bring new phases of matter that exhibit new properties reflecting the new organization. Rigidity, magnetism, liquid crystallinity, and superconductivity are just a handful of examples of such properties, which we call emergent collective properties. Until recently, organization meant geometry: Picture the tidy lattice of ions in a crystal of table salt. Nowadays, however, in the light of the elegant ideas put forward by David Thouless, Duncan Haldane, Mike Kosterlitz, and the many they have inspired, physicists recognize that organization can be subtler and more elusive. It can be invisible to geometry, though detectable via topology, and still trigger revolutions in the human-scale properties that make matter useful. My aim is to spend fifty minutes at the intersection of beauty and impact. I shall introduce the circle of ideas that underlie classical and quantum phases of matter and then focus on the “theoretical discoveries of topological phase transitions and topological phases of matter” that the 2016 Nobel Prize in Physics is celebrating.