晶格上激子的变分离散变量表示
Variational discrete variable representation for excitons on a lattice
摘要：
我们在一个格点上构造数值基函数集，其空间扩展可以从单个格点扩展到连续极限。它们使我们能够以相当的、适度的努力来计算小的和大的束缚态。采用离散变量表示的概念，通过对高斯求积点的酉变换，得到了势项的对角形式。因此，三维中的计算工作量按比例缩放为沿每个轴的基函数的数量的四次方而不是六次方，使得其在现实示例中减少了两个数量级。作为对标准离散变量表示的改进，我们的构造保留了变分原理。它允许计算结合能，波函数，和激发光谱。我们使用这种技术来研究中央电池的激子修正超越连续近似。本文在简单晶格模型的基础上讨论了氧化亚铜中不遵循Mott-Wannier激子类氢Rydberg系列的黄色激子系列的质量和光谱。
英文摘要：
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.
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