Quantum critical electron systems: the uncharted sign worlds.

Phases of classical matter, such as solids and liquids, are ruled by emergence principles that are well understood. Although the same principles govern forms of quantum matter that have no secrets for physicists, such as the superfluids, having to deal with fermions and the associated Fermi sign problem shatters this analogy. This Perspective addresses the Fermion sign problem and describes experiments on metals undergoing quantum phase transitions exhibiting scale-invariant electronic behavior, a description of which is at odds with established quantum theory.