Oxford Quantum Condensed Matter Theory Grant

Condensed matter physics is the science of the material world around us. When one examines materials on the smallest scales - their atoms and electrons - inevitably, quantum mechanics comes into play. The study of how properties of matter depend on quantum physics is the purview of quantum condensed matter theory, and the topic of this research programme. Over the last hundred years, many of the most important advances in technology owe their existence to fundamental breakthroughs in quantum condensed matter theory: The invention of the transistor, which resulted in the modern computer industry, depended on an understanding of the quantum theory of electrons in solids; the development of the laser, which resulted in modern optical communication networks, relied on the understanding of quantum properties of light in solids; magnetic resonance imaging, a key tool of modern medicine, came only after many years of study of the properties of magnetism on the quantum level. Perhaps the central question in this field, and in all of condensed matter physics, is how to describe physical systems with many constituent pieces -such as many electrons in a solid - which are all interacting with each other. While such systems with many pieces are impossibly complex - it is entirely hopeless to describe the motions of all of the pieces - the last century of physics has taught us that simplicity and structure is frequently behind the complex. It is 'just' a matter of finding the right description. Surprisingly, the simple structure which arises from the many interacting pieces can be radically different from the structure of the underlying constituents. Such so-called emergent phenomena , are a major focus of condensed matter theory in general. A dramatic example of this is given by fractional quantum Hall physics, where a fluid made up entirely of electrons, quantum mechanically conspires to produce particles with only a third of the charge of a single electron. The implications of emergent phenomena are far reaching, and raise questions about the ubiquity of the reductionist philosophy that has implicitly dominated much of physics for most of the last century - the view that the best route to understanding is to divide and study pieces individually. The Oxford quantum condensed matter theory group applies a wide range of theoretical approaches to some of the most important outstanding questions in the field. While the individual projects may differ in detail, they are deeply connected by the search for emergent structure and simplicity in otherwise complex quantum many-particle systems. They are further united by several common sub-themes: (i) The study of non-equilibrium quantum many-body systems, i.e., quantum mechanical systems of many particles where the well-known and well-understood theoretical structures based on thermodynamics fail to apply. (ii) The study of collective behaviour of electrons in nanoscale systems, where strongly interacting many-particle physics meets the quantum world on the near-molecular scale.(iii) The study of unconventional orders, which are emergent structures, like the fractional quantum hall effect, where new structure (or order ) arises that is very different from that of the constituent pieces. We firmly believe that continued study in these exciting theoretical directions will lead to the opening of new possibilities for the technologies of the future - in the same way that the last century of theoretical condensed matter physics has unquestionably done.

Many of the technological revolutions of the last century had their primary origins in our increased understanding of quantum condensed matter on a microscopic scale. The modern computer industry, optical communication networks, and magnetic resonance imaging -- whose influence of society has been transformative -- arose from fundamental breakthroughs in understanding the quantum theory of electrons, light and magnetism in condensed matter. The work proposed in this programme of research has, in the long term, the potential to benefit society in a similar way. The projects concerned with topological phases of matter, for example, are directly aimed at developing a quantum information processing device - an aim already shared by Microsoft research, with whom we work closely. If this can be achieved it will certainly revolutionize information technology, enabling exponential speedups in such tasks as decryption and quantum level simulations, with application eg to drug and materials design. Another example is Kondo and related physics in quantum dots, which explores circuitry on the single electron level. Any further miniaturization of current day semiconductor circuitry will inevitably come up against quantum mechanical effects which remain poorly understood. A hope is that the strange quantum effects currently being studied in these systems can be harnessed and functionalized in future technologies. The large international community of researchers working on quantum condensed matter will naturally be major beneficiaries of our work and its outputs. Other direct beneficiaries include students and postdoctoral researchers of the highest international calibre, who come from around the world to work with us and study under our tutelage. We train our students and PDRAs to think independently and critically, and provide them with a sound scientific training and the ability to solve problems using high level reasoning, analytic and computational skills. Our students and PDRAs will, as they have done in the past, become the university faculty, leaders of industry and decision makers of the future. To ensure that our results reach their target audiences they will be disseminated in leading journals. We, and in many cases our PDRAs, receive many invitations to speak at conferences. We will also continue to reach a wider audience by summarizing our work in review articles, summer school lectures, notes and books. Scientific understanding, given due dissemination, also has an important role to play in enriching the quality of life, in a way analogous to music or art. If the general public is more aware of the wonders of modern science they will view the world around them very differently, with a potential result of rebalancing our economy towards a more technology driven one. In this respect we are also involved in presenting our work to the wider public. For example, SHS has given the prestigious Heinz Pagels memorial lecture in Aspen, Colorado and has also written for the more general public, eg in Physics World.