Development of systematically improvable novel computational methods for strongly correlated quantum many-body problems in extended systems

My primary research question is, how can we improve upon existing methods used to examine extended systems. While existing methods have had significant success in predicting some strongly correlated system; certain systems, unique circumstances and particular quantities have struggled to be captured by these models. This has typically been due to one of three factors; computational cost, accuracy and unincorporated physics. When developing a method, it is challenging to optimise for more than one or two of these factors. Thus novel methods are required for these cases.

I have recently been focused on a novel approach to the GW approximation in an upfolded representation which systematically approximates the excitation energies through a series of static spectral moments. This moment-based GW implementation was initially explored in molecular systems with random phase approximation level screening. Since its inception the method has expanded to include native support for solids, Tamm-Dancoff approximation screening and a variety of self-consistency implementations whilst avoiding analytic continuation or the Matsubara axis to converge quantities at zero temperature. An implementation that reduces the scaling from O(N^4) to O(N^3) is examined, while finite size corrections are implemented to maintain the accuracy of small k-point mesh calculations without increasing the scaling of the solids implementation.