Title: Projected Hartree Fock Theory as a Polynomial Similarity Transformation Theory of Single Excitations Show Chinese title

Title: 投影哈特里-福克理论作为单激发的多项式相似变换理论

Abstract: Spin-projected Hartree-Fock is introduced as a particle-hole excitation ansatz over a symmetry-adapted reference determinant. Remarkably, this expansion has an analytic expression that we were able to decipher. While the form of the polynomial expansion is universal, the excitation amplitudes need to be optimized. This is equivalent to the optimization of orbitals in the conventional projected Hartree-Fock framework of non-orthogonal determinants. Using the inverse of the particle-hole expansion, we similarity transform the Hamiltonian in a coupled-cluster style theory. The left eigenvector of the non-hermitian Hamiltonian is constructed in a similar particle-hole expansion fashion, and we show that to numerically reproduce variational projected Hartree-Fock results, one needs as many pair excitations in the bra as the number of strongly correlated entangled pairs in the system. This single-excitation polynomial similarity transformation theory is an alternative to our recently presented double excitation theory, but supports projected Hartree-Fock and coupled cluster simultaneously rather than interpolating between them. Show Chinese abstract

Abstract: 自旋投影的哈特里-福克方法被引入为对一个对称适应的参考行列式进行粒子-空穴激发的假设。值得注意的是，这种展开具有我们能够解析解出的表达式。虽然多项式展开的形式是通用的，但激发振幅需要进行优化。这等价于在非正交行列式的传统投影哈特里-福克框架中对轨道进行优化。利用粒子-空穴展开的逆，我们以耦合簇理论的方式对哈密顿量进行相似变换。非厄米哈密顿量的左本征向量以类似的粒子-空穴展开方式构建，并且我们证明为了数值再现变分投影哈特里-福克结果，需要在bra中包含与系统中强关联纠缠对数量相同的一对激发。这种单激发多项式相似变换理论是我们最近提出的双激发理论的替代方案，但它同时支持投影哈特里-福克和耦合簇，而不是在两者之间插值。