Variational discrete variable representation for excitons on a lattice

Abstract

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.

Modeling of the thermalization of trapped paraexcitons inCu2Oat ultralow temperatures

“…The binding energies of the yellow and green paraexcitons are approximately equal [19] and hence do not appear in Eq. (A2) explicitly.…”

High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

“…This prevents the use of direct solvers such as PARDISO [22] or ILUPACK [23], which have been used successfully for, e.g., Anderson localization [21]. In some applications the matrix is not even stored explicitly but constructed 'on-thefly' [24,25]. Therefore, we assume that the only feasible sparse matrix operation in ChebFD is sparse matrix vector multiplication (spMVM).…”

Time-resolved cyclotron resonance in cuprous oxide

“…14 Also, a computational study, which requires the electron and hole effective masses as known parameters, has shown that the central-cell corrections account for the large excitonic mass. 15 Since the excitonic mass is a key parameter determining the critical temperature for a quantum phase transition, such as Bose-Einstein condensation, solving the controversy on the hole effective mass is important.…”