School of Chemistry, University of Leeds, Leeds LS2 9JT, United Kingdom.
J Chem Phys. 2018 May 21;148(19):194109. doi: 10.1063/1.5023209.
Canonical Coherent States (CSs) of Harmonic Oscillator have been extensively used as a basis in a number of computational methods of quantum dynamics. However, generalising such techniques for fermionic systems is difficult because Fermionic Coherent States (FCSs) require complicated algebra of Grassmann numbers not well suited for numerical calculations. This paper introduces a coherent antisymmetrised superposition of "dead" and "alive" electronic states called here Zombie State (ZS), which can be used in a manner of FCSs but without Grassmann algebra. Instead, for Zombie States, a very simple sign-changing rule is used in the definition of creation and annihilation operators. Then, calculation of electronic structure Hamiltonian matrix elements between two ZSs becomes very simple and a straightforward technique for time propagation of fermionic wave functions can be developed. By analogy with the existing methods based on Canonical Coherent States of Harmonic Oscillator, fermionic wave functions can be propagated using a set of randomly selected Zombie States as a basis. As a proof of principles, the proposed Coupled Zombie States approach is tested on a simple example showing that the technique is exact.
简正相干态（CSs）在许多量子动力学的计算方法中被广泛用作基础。然而，将这种技术推广到费米子系统是困难的，因为费米子相干态（FCSs）需要复杂的格拉斯曼数代数，不适合数值计算。本文引入了一种被称为僵尸态（ZS）的“死”和“活”电子态的相干反演叠加，它可以像 FCSs 一样使用，但没有格拉斯曼代数。相反，对于僵尸态，在定义产生和湮灭算符时使用非常简单的符号变化规则。然后，两个 ZS 之间的电子结构哈密顿矩阵元的计算变得非常简单，可以开发出一种用于费米子波函数时间传播的直接技术。通过与基于简正相干态的现有方法类比，可以使用一组随机选择的僵尸态作为基来传播费米子波函数。作为原理的证明，所提出的耦合僵尸态方法在一个简单的示例上进行了测试，表明该技术是精确的。
