Hyper-sparsity of the density matrix in a wavelet representation

Details Hyper-sparsity of the density matrix in a wavelet representation Hyper-sparsity of the density matrix in a wavelet representation

1998-06-05

arxiv.org/abs/cond-mat/9806069v1

Physics

Condensed Matter

4 color figures, 3 normal figures

Scientific paper

O(N) methods are based on the decay properties of the density matrix in real space, an effect sometimes refered to as near-sightedness. We show, that in addition to this near-sightedness in real space there is also a near-sightedness in Fourier space. Using a basis set with good localization properties in both real and Fourier space such as wavelets, one can exploit both localization properties to obtain a density matrix which exhibits additional sparseness properties compared to the scenario where one has a basis set with real space localization only. We will call this additional sparsity hyper-sparsity. Taking advantage of this hyper-sparsity, it is possible to represent very large quantum mechanical systems in a highly compact way. This can be done both for insulating and metallic systems and for arbitrarily accurate basis sets. We expect that hyper-sparsity will pave the way for O(N) calculations of large systems requiring many basis functions per atom, such as Density Functional calculations.

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