Accelerating Strongly Correlated Electronic Structure Calculations Using Real-Space Renormalization Group Techniques and Density Functional Theory

In many-body physics, the renormalization group (RG) allows one to perform changes of scale to observe emergent physical properties. Similarly, wavelet transforms (WTs), a popular data-compression technique in signal processing, are an analysis tool used to find correlations in data at different scales. There have been many recent developments showing that WTs correspond exactly to a real-space RG transformation. An entire class of novel WTs have been created using RG techniques with many desirable qualities that traditional WTs do not. Here we use these novel WTs as a coarse-graining protocol for strongly correlated electronic structure calculations. The benefit of this protocol is two-fold; each WT results in a coarsening by a factor of 3 but maintains a minimal loss in accuracy due to the highly localized nature and orthogonality of the wavelets, making electron-electron repulsion approximations much better. Using these techniques, we can obtain milliHartree accuracy in the ground state energy for standard atomic calculations in 1D, such as He, C, and BeH₂. Preliminary work also shows that system-adapted WTs can increase accuracy even further. This work suggests that using WTs can be used to effectively reduce exponential scaling in electronic structure calculations.