The set of all electronic states that can be expressed as a single Slater determinant forms a submanifold, isomorphic to the Grassmannian, of the projective Hilbert space of wave functions. We explored this fact by using tools of Riemannian geometry of Grassmannians as described by Absil et. al [Acta App. Math. 80, 199 (2004)], to propose an algorithm that converges to a Slater determinant that is critical point of the overlap function with a correlated wave function. This algorithm can be applied to quantify the entanglement or correlation of a wave function. We show that this algorithm is equivalent to the Newton method using the standard parametrization of Slater determinants by orbital rotations, but it can be more efficiently implemented because the orbital basis used to express the correlated wave function is kept fixed throughout the iterations. We present the equations of this method for a general configuration interaction wave function and for a wave function with up to double excitations over a reference determinant. Applications of this algorithm to selected electronic systems are also presented and discussed.
在反对称子空间$\wedge^ N \bC^M$中，利用Slater行列式作为乘积态的模拟，讨论了费米子系统的不可扩展乘积基（UPB）和广义UPB的概念.我们构造了一个明确的例子，广义费米子不可扩展的产品基（FUPB）的最小基数$N(M-N)+1$的任何$N\ge2,M\ge4$。我们还证明了任何余维为2的二分反对称空间$\wedge^ 2 \bC^M$都被Slater行列式张成，而更高余维的空间不一定被Slater行列式张成。此外，我们构造了一个具有最小基数$5$的$N=2,M=4$的复FUPB的例子。相反，我们表明，一个真正的FUPB不存在$N=2,M=4$。最后，我们提供了一个系统的建设，更高的维度FUPBs使用FUPBs和UPBs的低维。
Generalization of Brillouin theorem for the non-relativistic electronic Schrödinger equation in relation to coupling strength parameter, and its consequences in single determinant basis sets for configuration interactions
Quantum Monte Carlo description of correlated electrons in two-dimensional FeSe
University of Manchester（曼彻斯特大学）；Tohoku University（东北大学）；Center for Advanced Systems Understanding（先进系统理解中心）；Helmholtz Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；TU Dresden（德累斯顿工业大学）
