Are Itinerant-Electron Quantum Critical Points Intrinsically Multicritical?

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The electronic behaviour of apparently simple solids can have enormous technological impact. To take a recent example, the giant magnetoresistance of certain layered materials rapidly moved from experimental discovery to theoretical understanding and then to the scientific underpinning of modern hard drives. As well as its technological importance, the occurrence of such unanticipated behaviour in apparently simple materials provides a vital experimental window upon fundamental physics.A central challenge facing theoretical physicists is to determine the collective quantum behaviour of many interacting electrons. There have been notable successes along the way- the theory of Landau and Fermi (known as Landau-Fermi-liquid theory) showed that in many situations, even if the electrons interact strongly, they behave almost as though they were not interacting, but with modified individual characteristics. However, a large (and increasing) number of materials have been discovered whose electronic behaviour cannot be described by the Landau-Fermi-liquid theory. Physicists have struggled to formulate a unified picture to explain these non-Fermi liquid materials. A great leap forwards was made with the formulation of the theory of quantum criticality. This theory describes the behaviour of systems that are finely balanced between classical and quantum behaviour- usually systems that are near to a zero-temperature magnetic phase transition i.e. systems that show a change from magnetic to non-magnetic behaviour as some parameter such as pressure is varied at close to absolute zero. A large number of materials appear to be described by the theory of quantum criticality.In recent years, problems have been found in this theory. Whenever one tries to perform experiments very close to the point at zero temperature where the transition in magnetic behaviour ought to occur, one finds something very different- often the electrons are organised in a completely different way. At the same time, theoretical physicists have realised that the mathematics which was thought to describe the magnetic quantum phase transition is not self-consistent. This inconsistency is not minor --- it suggests a fundamental breakdown in our understanding of strongly correlated systems. The hope amongst physicists is that in resolving these issues a new broader understanding of the nature of collective quantum behaviour will result. This is a particularly fruitful time for such investigations as a number of theoretical and experimental ingredients are in place and ripe for combining to form the new theory.These ideas apply not only to electron systems, but also to other systems with many interacting quantum particles. The investigation of ultra-cold atoms confined by a combination of lasers and magnetic fields presents perhaps a cleaner forum for the experimental investigation of these ideas. As indicated above, not only is this work important our fundamental understanding of the world, it is also likely to feed directly into technology. As our manipulation of the nano-world leads us further and further into the quantum realm, it is imperative that we understand its nature.