Are Itinerant-Electron Quantum Critical Points Intrinsically Multicritical?

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.

Skills Base: One of the key contributions of our research programme will be to the UK skills base. This benefit will be felt on several levels a) UK Science: The UK has a world-leading effort in the experiments on quantum critical systems. This is coordinated through programmes such as the EPSRC Portfolio Partnership Novel Quantum Order in Interacting Electron Metals . An important aim of this proposal is to build upon this success by coordinating key theoretical efforts in this area. The enhanced profile will benefit UK science and advertise the breadth of the UK skills base. b) Post-doctoral Fellows: It will afford post-doctoral research fellows the opportunity to develop both cutting edge theoretical skills and the ability to apply them in practice to real experiments. Precisely the same skills are essential in modern industry. The post-doctoral research fellows will learn the skills necessary to engage with both the local and broader research group and manage these interactions towards key scientific goals. This will be fostered by the periodic meetings of the researchers funded by this grant and face-to-face interaction with our broader international network of collaborators. We are well-placed to guide them towards contacts in both academia and the financial services and technology sectors. These benefits will accrue over the Post-doctoral fellows' appointments and have a legacy throughout their careers. c) PhD Students: More than half of this programme will be carried out in the University of St Andrews - one of the host institutions for the Scottish Doctoral Training Centre in Condensed Matter Physics. It is essential for the success of the DTC that it is embedded within world-class research groups. Our team will form an important part of this environment and will help to enhance the theoretical training of graduate students. We will have a particularly strong impact in this area since one of us (CAH) is the director of teaching for the DTC. Our research team will benefit from the elite graduate students that the DTC attracts and from its programme of international scientific visitors. The 29 graduate students in Loughborough work almost exclusively on condensed matter and will benefit greatly from the Post-doctoral fellow based there. The benefits of this will impact throughout the careers of the students, whether in science or industry. Materials and Technology: Although focused on fundamental physics, the work proposed here is likely to have longer term, technological impact. Strongly correlated electron materials will play a key role in future technologies. As usual in such a cutting edge area of research, experimental and theoretical progress occur in tandem - a strong argument for developing and maintaining complementary skills bases in both theoretical and experimental research. The timing and extent of this impact is impossible to judge in advance of discovery, but it is essential for future industry. Public Outreach: The proposers are particularly active in public outreach including presentations in Schools and Colleges, the Royal Institution, various Cafes Scientifique and running local outreach organisations. These activities will be coordinated with outreach activities of the DTC and the Gateway to Physics programme organised jointly between St Andrew and Heriot Watt. The Loughborough Physics Centre aims to bring physics to the general public through lectures and demonstrations and will provide an excellent public outlet for our work. This has a dual role: By inspiring young students with new discoveries and informing them of possible careers, these activities help to develop the skills base in science and technology. These are exciting times in theoretical physics with new links being forged between apparently disparate areas such as string theory, black holes and the quantum critical systems that we propose to study. We aim to share this excitement with the public.