Methods of Calculation with the Exact Density Functional using the Renormalization Group
- Author(s): Baker, Thomas Edward
- Advisor(s): Burke, Kieron
- White, Steven R
- et al.
Solving Schrodinger's equation is extremely important to determine the quantum mechanical properties of a material and model chemistry computationally. Density functional theory is one of the best scaling methods for large numbers of particles and can be used as a tool to investigate large quantum systems, but this method requires approximation in practice, leading to approximate answers. The exact density functional theory is still useful for investigation, despite not having the exact universal functional for all cases so the theory can be better understood. Here, we analyze the properties of the exact theory by accessing the exact functional. We do so by constructing a situation where this is possible: in one dimension with the aid of the density matrix renormalization group and machine learning techniques. This toolset is used to study the properties of the convergence of the exact functional. Important for any technique is how the problem is phrased in a particular basis, and we combine the methods of the renormalization group, through a family of transformations called wavelets, with density functional calculations to determine an optimized basis set with wavelets for a given quantum computation.