Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2011-04-05
Phys. Rev. B 84, 035126 (2011)
Physics
Condensed Matter
Other Condensed Matter
12 pages, 7 figures. Final version as published
Scientific paper
10.1103/PhysRevB.84.035126
We construct numerical basis function sets on a lattice, whose spatial extension is scalable from single lattice sites to the continuum limit. They allow us to compute small and large bound states with comparable, moderate effort. Adopting concepts of discrete variable representations, a diagonal form of the potential term is achieved through a unitary transformation to Gaussian quadrature points. Thereby the computational effort in three dimensions scales as the fourth instead of the sixth power of the number of basis functions along each axis, such that it is reduced by two orders of magnitude in realistic examples. As an improvement over standard discrete variable representations, our construction preserves the variational principle. It allows for the calculation of binding energies, wave functions, and excitation spectra. We use this technique to study central-cell corrections for excitons beyond the continuum approximation. A discussion of the mass and spectrum of the yellow exciton series in the cuprous oxide, which does not follow the hydrogenic Rydberg series of Mott-Wannier excitons, is given on the basis of a simple lattice model.
Alvermann Andreas
Fehske Holger
Littlewood Peter B.
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