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

近年来，格林小组开发了一种新的方法来理解量子涨落如何在具有可能有用的性质的固体中诱导新的电子相。这种被称为费米子无序量子有序的方法在很大程度上是分析性的，为一系列量子现象提供了一个很好的定性解释。虽然易于分析的模型在对新现象的定性理解中发挥着重要作用，但有时需要精确的数值预测--特别是在指导实验通过相互竞争的可能性的微妙平衡时。目前，涨落诱导效应的计算，如超导电性，是与从头算能带结构计算并行进行的；后者提供了场理论Eliashberg型方程中使用的自旋磁化率。如果这些计算能够协调一致地进行，那将是很有吸引力的。QOBD建议了一种自然的方式来做到这一点。它很好地处于一个框架内，该框架将DFT、DMFT和Baym-Kadanoff理论置于一个统一的背景下。我们的QOBD公式本质上是对Baym-Kadanoff理论的限制，在该理论中，变分参数-格林函数-本身由一组受限的参数来表征。我们的目标是将QOBD引入DFT，使我们能够在相同的数值框架内研究密度波、电子向列相、空间调制磁序和超导电性。为了探索这种可能性，克里斯·皮卡德教授(CJP Cambridge)和AGG将结合他们互补的数值和分析技能，共同监督博士项目。该项目将是评估这一方法可行性的试验性研究。预计不会立即实现商业化。

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.