论文标题
理查森 - 戈丁州的密度矩阵降低了Gaudin代数的基础
Reduced density matrices of Richardson-Gaudin states in the Gaudin algebra basis
论文作者
论文摘要
降低的Bardeen-Cooper-Schrieffer Hamiltonian的特征向量最近被用作量子化学中的差异波函数ANSATZ。该波函数是一对电子（Geminals）的平均场。在此贡献中，我们报告了其原始物理基础和理查森 - 戈丁对基础的最佳表达式。 Gorohovsky和Bettelheim最初报道了物理基础表达。在每种情况下，表达式比例像$ \ MATHCAL {O}（n^4）$，最昂贵的步骤是线性方程的解决方案。分析梯度也会在物理基础上报告。这些表达式是迈向实用的均值方法来处理强相关电子的重要一步。
Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian have recently been employed as a variational wavefunction ansatz in quantum chemistry. This wavefunction is a mean-field of pairs of electrons (geminals). In this contribution we report optimal expressions for their reduced density matrices in both the original physical basis and the basis of the Richardson-Gaudin pairs. Physical basis expressions were originally reported by Gorohovsky and Bettelheim. In each case, the expressions scale like $\mathcal{O}(N^4)$, with the most expensive step the solution of linear equations. Analytic gradients are also reported in the physical basis. These expressions are an important step towards practical mean-field methods to treat strongly-correlated electrons.
