For over three decades, physicists have successfully understood the properties of a variety of solid-state materials using what is essentially an independent-electron picture, along with sophisticated variants. This understanding has been exploited in a large number of technological advances that influence our everyday lives. One important frontier in the study of new materials now lies in systems in which such a simple picture fails and strong correlations abound. The electron correlations in the magnetic insulators, high-temperature superconductors and quantum Hall systems described in this article are just a few examples of this.
A powerful theoretical handle on such systems is to identify the quantum critical points between various zero-temperature phases, and to use these critical points as a vantage point for exploring the rest of the phase diagram. It is clear that we have just scratched the surface of much exciting progress to come.