论文标题
理查森 - 高丁氏态降低密度矩阵 /静态相关函数，没有速度
Reduced Density Matrices / Static Correlation Functions of Richardson-Gaudin States Without Rapidities
论文作者
论文摘要
众所周知，零元的Geminal波函数可捕获断裂的相关性。在这类波段中，理查森·戈丁国家（Richardson-Gaudin）脱颖而出，因为它们是哈密顿模型的特征向量。这提供了清晰的物理图片，用于减少密度矩阵（RDM）元素的干净表达方式以及系统的改进（具有完整的特征向量）。 RDM元素的已知表达式需要计算速度，这是通过首先解决所谓的基于特征值的变量（EBV），然后对拉格朗日插值多项式的根找到。在本手稿中，我们直接根据EBV获得了RDM元素的表达式。最终表达式可以以与速度表达式相同的成本计算。因此，除了在特定情况下，完全没有必要计算速度。 RDM元素需要在数值上反转矩阵，尽管这通常是不希望的，但我们证明它是稳定的，除非单粒子能量中存在变性。在这种情况下，需要不同的结构。
Seniority-zero geminal wavefunctions are known to capture bond-breaking correlation. Among this class of wavefunctions, Richardson-Gaudin states stand out as they are eigenvectors of a model Hamiltonian. This provides a clear physical picture, clean expressions for reduced density matrix (RDM) elements, and systematic improvement (with a complete set of eigenvectors). Known expressions for the RDM elements require the computation of rapidities, which are obtained by first solving for the so-called eigenvalue based variables (EBV) then root-finding of a Lagrange interpolation polynomial. In this manuscript we obtain expressions for the RDM elements directly in terms of the EBV. The final expressions can be computed with the same cost as the rapidity expressions. Therefore, except in particular circumstances, it is entirely unnecessary to compute rapidities at all. The RDM elements require numerically inverting a matrix and while this is usually undesirable we demonstrate that it is stable, except when there is degeneracy in the single-particle energies. In such cases a different construction would be required.
