Targeting specific eigenvectors and eigenvalues of a given Hamiltonian using arbitrary selection criteria

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Date

2002-12

Journal Title

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Volume Title

Publisher

American Physical Society

Abstract

We present a method for calculating some select eigenvalues and corresponding eigenvectors of a given Hamiltonian. We show that it is possible to target the eigenvalues and eigenvectors of interest without diagonalizing the full Hamiltonian, by using any arbitrary physical property of the eigenvectors. This allows us to target, for example, the eigenvectors based on their localization properties (e.g., states localized at a given surface or interface). We also show that the method scales linearly with system size.

Description

Keywords

quantum dots, large matrices, pseudopotentials, algorithms, iteration, lowest, energy, physics, condensed matter

Citation

Tackett, A. R.; Di Ventra, M., "Targeting specific eigenvectors and eigenvalues of a given Hamiltonian using arbitrary selection criteria," Phys. Rev. B 66, 245104 DOI: http://dx.doi.org/10.1103/PhysRevB.66.245104