论文标题
2D-block Geminals：一种非1个正交和非0元素模型，计算复杂性降低
2D-Block Geminals: a non 1-orthogonal and non 0-seniority model with reduced computational complexity
论文作者
论文摘要
我们提出了一种新的Geminal产品波函数ANSATZ，其中Geminals不受约束为正交的，也不是零。取而代之的是，我们在Geminal之间引入了较弱的正交性约束，这些束缚大大降低了计算工作，而无需牺牲电子的不可区分性。也就是说，对应于Geminals的电子对无法完全区分，并且仍必须根据Pauli原理对它们的产物进行反对称，以形成A \ TextIt {Bona fide}电子波函数。它的几何约束将转化为简单的方程式，这些方程涉及我们的Geminal Matrices产品的产物。在最简单的非平凡模型中，一组解决方案由块对基矩阵给出，其中每个块的大小为2x2，由Pauli矩阵或归一化的对角线矩阵组成，乘以要优化的复杂参数。通过这种简化的geminal ansatz，量子观测值的矩阵元素计算中的项数量大大减少了。报告了原理证明，并确认ANSATZ比强烈的正交Geminal产品更准确，同时保持计算负担得起。
We present a new geminal product wave function ansatz where the geminals are not constrained to be strongly orthogonal nor to be of seniority zero. Instead, we introduce weaker orthogonality constraints between geminals which significantly lower the computational effort, without sacrificing the indistinguishability of the electrons. That is to say, the electron pairs corresponding to the geminals are not fully distinguishable, and their product has still to be antisymmetrized according to the Pauli principle to form a \textit{bona fide} electronic wave function.Our geometrical constraints translate into simple equations involving the traces of products of our geminal matrices. In the simplest non-trivial model, a set of solutions is given by block-diagonal matrices where each block is of size 2x2 and consists of either a Pauli matrix or a normalized diagonal matrix, multiplied by a complex parameter to be optimized. With this simplified ansatz for geminals, the number of terms in the calculation of the matrix elements of quantum observables is considerably reduced. A proof of principle is reported and confirms that the ansatz is more accurate than strongly orthogonal geminal products while remaining computationally affordable.
