Generalized Pauli conditions on the spectra of one-electron reduced density matrices of atoms and molecules
Generalized Pauli conditions on the spectra of one-electron reduced density matrices of atoms and molecules
复制标题
原子和分子单电子约化密度矩阵光谱的广义泡利条件
DOI：
10.1103/physreva.89.042505
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发表时间：
2014
影响因子：
2.9
通讯作者：
D. Mazziotti
中科院分区：
文献类型：
--
作者：
Romit Chakraborty;D. Mazziotti
泡利不相容原理要求单电子约化密度矩阵（1-RDM）的占据数的谱以1和0为界。然而，对于来自波函数的1-RDM，在占据数的谱上存在额外的条件，称为纯N-可表示性条件或广义泡利条件。对于原子和分子，我们测量通过欧几里德距离度量的1-RDM光谱的面的凸集（多面体）所产生的广义泡利条件的接近。对于任意自旋对称性的基态，只要在多面体的定义中考虑时间反演对称性，我们发现1-RDM的谱被钉扎在多面体的边界上。相反，对于激发态，我们发现1-RDM谱不是钉扎的。1-RDM到多面体边界的接近度提供了量子系统内电子相关和纠缠的测量和分类。为了进行比较，还将到广义泡利条件的边界的距离与到传统泡利条件的多面体的距离以及到来自斯莱特行列式的最近的1-RDM谱的距离进行比较。我们解释了在地面和激发态1-RDM钉扎的差异，通过连接到N-representability条件的两个电子约化密度矩阵。
The Pauli exclusion principle requires the spectrum of the occupation numbers of the one-electron reduced density matrix (1-RDM) to be bounded by one and zero. However, for a 1-RDM from a wave function, there exist additional conditions on the spectrum of occupation numbers, known as pure N-representability conditions or generalized Pauli conditions. For atoms and molecules, we measure through a Euclidean-distance metric the proximity of the 1-RDM spectrum to the facets of the convex set (polytope) generated by the generalized Pauli conditions. For the ground state of any spin symmetry, as long as time-reversal symmetry is considered in the definition of the polytope, we find that the 1-RDM's spectrum is pinned to the boundary of the polytope. In contrast, for excited states, we find that the 1-RDM spectrum is not pinned. Proximity of the 1-RDM to the boundary of the polytope provides a measurement and classification of electron correlation and entanglement within the quantum system. For comparison, this distance to the boundary of the generalized Pauli conditions is also compared to the distance to the polytope of the traditional Pauli conditions, and the distance to the nearest 1-RDM spectrum from a Slater determinant. We explain the difference in pinning in the ground- and excited-state 1-RDMs through a connection to the N-representability conditions of the two-electron reduced density matrix.