MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Wavelet Approach to Quasi Two-Dimensional Extended Many-Particle Systems. I. Supercell Hartree-Fock Method

Heinz-Jürgen Flad, Wolfgang Hackbusch, Hongjun Luo and Dietmar Kolb


We propose a wavelet based multiresolution Hartree-Fock method suitable for quasi two-dimensional extended systems. Intended applications are metallic slabs and excitons confined in quantum wells of semiconductor heterostructures. The method uses a periodic supercell approach, which allows for an incorporation of single impurities. Special emphasis has been laid on low rank tensor product decompositions of orbitals, which take into account the strongly anisotropic character of these systems in one direction. Wavelets provide hierarchical bases that can be adapted to the anisotropic behaviour of the orbitals. We discuss some technical features related to the wavelet expansion of Ewald potentials, which are used to describe the interaction between particles. Due to the vanishing moment property of wavelets, we can achieve sparse representations for the quantities involved. An illustrative example for this are jellium slabs, where we discuss various sparsity features of matrices related to Coulomb and exchange potentials. Benchmark calculations for a homogeneous electron gas finally demonstrate the computational feasibility and numerical accuracy of our approach.

MSC Codes:
65R20, 65T60, 81Q05
wavelets, hartree-fock

Related publications

2005 Repository Open Access
Heinz-Jürgen Flad, Wolfgang Hackbusch, Hongjun Luo and Dietmar Kolb

Wavelet approach to quasi two-dimensional extended many-particle systems. Pt. 1 : Supercell Hartree-Fock method

In: Journal of computational physics, 205 (2005) 2, pp. 540-566