Methods Development
In the McMahon Research Group, we model condensed matter starting from the fundamental equations of quantum mechanics. Except for the most simple systems, these are impossible to solve analytically. We therefore apply computational methods; typically, we use either quantum Monte Carlo (QMC), which can (in principle) find exact solutions, or density-functional theory (DFT), which is approximate, but with a much lower computationally cost.
The computational cost of QMC and/or accuracy of DMC, however, limit their applicability. We therefore look for ways in which to improve the accuracy and efficiency of quantum simulation methods. Of recent interest is the use of machine learning in computational physics.
Image coming soon
Machine Learning
There are several problems in computational physics for which accurate and efficient algorithms for their solution are unknown. A recent interest of ours has been to consider ways in which techniques and theory in and from the emerging field of data science can be used to solve such open, currently intractable problems. An example is the approximation to the universal, but unknown exchange–correlation density functional in DFT. We have recently developed a method based on deep learning (machine learning) can be used to determine the functional form of this unknown functional (manuscript in preparation).