Hyper-sparsity of the density matrix in a wavelet representation
| dc.creator | Goedecker, S. | |
| dc.creator | Ivanov, O. V. | |
| dc.date | 1998-06-05 | |
| dc.date.accessioned | 2026-07-07T03:10:46Z | |
| dc.date.available | 2026-07-07T03:10:46Z | |
| dc.description | 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. | |
| dc.description | 4 color figures, 3 normal figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9806069 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9806069 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/28330 | |
| dc.subject | Condensed Matter | |
| dc.title | Hyper-sparsity of the density matrix in a wavelet representation | |
| dc.type | text |