Wavelet-Based Multiscale Methods for Electronic Structure Calculations

Abstract

In order to treat multiple energy- and length-scales in electronic structure calculations for extended systems, we have studied a wavelet based multiresolution analysis of electron correlations. Wavelets provide hierarchical basis sets that can be locally adapted to the length- and energy-scales of physical phenomena. The inherently high dimensional many-body problem can be kept tractable by using the sparse grid method for the construction of multivariate wavelets. These so called “hyperbolic” wavelets provide sparse representations for correlated wavefunctions and can be combined with diagrammatic techniques from quantum many-particle theory into a diagrammatic multiresolution analysis. Using sparsity features originating from the hierarchical structure and vanishing moments property of wavelet bases, this leads to many-particle methods with almost linear computational complexity for the treatment of electron correlations.