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

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Submission date: 29. Sep. 2004
Pages: 31
published in: Journal of computational physics, 205 (2005) 2, p. 540-566 
DOI number (of the published article): 10.1016/j.jcp.2004.11.018
Bibtex
MSC-Numbers: 65R20, 65T60, 81Q05
Keywords and phrases: wavelets, hartree-fock
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Abstract:
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.