Fluctuation Induced Exotic Phases of Quantum Matter

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Usually fluctuations have a destabilising effect. When carrying a tray of drinks through a crowded room one wishes to avoid the jostling of the crowd. Similarly, a tightrope walker would probably avoid performing on a blustery day. However, there are many instances where fluctuations can have the opposite effect, stabilising a system in a configuration that might otherwise be unstable. This occurs when the noise is state-dependent; that is, when the spectrum of the fluctuating forces experienced by the system is modified by the particular configuration of the system. Examples include the balancing of a broom on ones fingertip - practice leads the expert to approach ever more closely to a Levy flight distribution of horizontal movements. The crucial point is that the torque experienced by the broom depends upon its angle to the vertical. Many other examples may be viewed in this way. For example, adaptable species, agile businesses and diverse investment strategies are all stable because of fluctuations in the environment.This phenomenon can also occur in quantum systems. In this case, the fluctuations concerned are intrinsic quantum fluctuations occurring because of Heisenberg's uncertainty principle. A quantum oscillator must always oscillate a little because of the uncertainty principle and so always carries a little energy, known as the zero-point energy. Changing the state of the system can change the frequency of these intrinsic quantum oscillations and so change the zero point energy. When the quantum fluctuations are very strong, reducing the zero point energy can be the main influence deciding the state that the system adopts. Applying this idea to metals with very strong quantum fluctuations has proven very useful in understanding novel states observed in experiment. Indeed, the observation of novel states has driven developments of aspects of the theory and the perspective suggested by the theory has suggested experiments. This proposal will continue to develop this approach - which has become known as fermionic quantum order-by-disorder. We aim to make progress in four key directions: - Extend the theoretical approach to new systems - Extend the accuracy of the theoretical approach - Explore novel quantum order experimentally - Experimental and Theoretical discovery