Quantum critical metals: Beyond the order parameter fluctuations

The standard description of quantum critical points takes into account only fluctuations of the order parameter, and treats quantum fluctuations as extra dimensions of classical fluctuations. This picture can break down in a qualitative fashion in quantum critical metals: non-Fermi liquid electronic excitations are formed precisely at the quantum critical point and appear as a part of the quantum-critical spectrum. In the case of heavy fermion metals, it has been proposed that the non-Fermi liquid behavior is characterized by the destruction of a Kondo effect. The latter invalidates Hertz's Gaussian theory of paramagnons and leads to an interacting theory that is "locally quantum critical". We summarize the theoretical and experimental developments on the subject. We also discuss their broader implications, and make contact with recent work on quantum critical magnets.