A significant part of modern physics research can be classified as the study of quantum matter. The aim is to describe the phases of large numbers of interacting particles at temperatures low enough that quantum mechanics plays a crucial role in determining the system’s distinguishing characteristics. For electrons in solids, the needed “low” temperatures can be even higher than room temperature. Gases of trapped atoms require ultracold temperatures in the nanokelvin range. And through collisions of heavy nuclei, groups at particle accelerators are pursuing a quantum plasma of quarks with temperatures approaching those realized soon after the Big Bang. Remarkably, a common set of ideas on the phases of quantum matter applies across that wide range of energy scales.

Electron systems in solids are one of the best places to study quantum matter. With modern fabrication techniques, one can make an almost infinite variety of crystals, which provide a rich...

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