

Preprint 65/2004
Toward diagrammatic multiresolution analysis for electron correlations
Heinz-Jürgen Flad, Wolfgang Hackbusch, Hongjun Luo, and Dietmar Kolb
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Submission date: 29. Sep. 2004
Pages: 36
published in: Physical review / B, 71 (2005) 12, art-no. 125115
DOI number (of the published article): 10.1103/PhysRevB.71.125115
Bibtex
with the following different title: Diagrammatic multiresolution analysis for electron correlations
PACS-Numbers: 71.15.-m, 71.10.Ca, 02.30.Mv
Keywords and phrases: wavelets, electron correlations
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Abstract:
We present a multiscale treatment of electron correlations based on
hyperbolic wavelet expansions of Jastrow-type correlation functions.
Wavelets provide hierarchical basis sets that can be locally adapted
to the length- and energy-scales of physical phenomena.
Combined with hyperbolic tensor products and local adaptive refinement near the inter-electron cusp,
these wavelet bases enable sparse representations of Jastrow factors.
The computational efficiency of wavelets in electronic structure calculations
is demonstrated within the coupled electron-pair approximation (local ansatz).
Based on a diagrammatic multiresolution analysis, we discuss
various kinds of sparsity features for matrix elements required by the local ansatz.
Sparsity originates from the hierarchical structure
and vanishing moments property of wavelet bases. This
led us to a recurrence scheme for the evaluation of matrix elements
with almost linear computational complexity with respect to the
size of the underlying isotropic 3d-wavelet basis.
Numerical studies for selected diagrams are presented for a
homogeneous electron gas.