Developing the fermionic quantum order by disorder approach to understanding novel quantum phases.

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In recent years the Green group has developed a new approach to understanding how quantum fluctuations can induce new phases of electrons in solids with possibly useful properties. This approach - known as fermionic quantum order by disorder is largely analytical providing a good qualitative account of a range of quantum phenomena. Whilst analytically tractable models play an important role in the qualitative understanding of new phenomena, sometimes numerically precise predictions are needed - particularly when guiding experiment through a delicate balance of competing possibilities. Presently, the calculation of fluctuation-induced effects, such as superconductivity, is carried out in parallel with ab initio band structure calculations; the latter providing spin susceptibilities that are used in field theoretical Eliashberg type equations. It would be appealing if these calculations could be performed in concert. QOBD suggests a natural way to do so. It sits nicely within the a framework , which places DFT, DMFT and Baym-Kadanoff theory in a unified context. Our formulation of QOBD is essentially a restriction of Baym-Kadanoff theory where the variational parameter - the Green's function - is itself characterised by a restricted set of parameters. We aim to incorporate QOBD into DFT, enabling us to study density wave, electron nematic, and spatially modulated magnetic order, and superconductivity all within the same numerical framework. To pursue this possibility, Prof Chris Pickard (CJP Cambridge) and AGG will combine their complementary numerical and analytical skills in joint supervision of the PhD project. This project will be a pilot study to asses the viability of this approach. No immediate commercialisation is expected.