Zombie states for description of structure and dynamics of multi-electron systems

Abstract

Perspective: Ab initio force field methods derived from quantum mechanics The Journal of Chemical Physics 148, 090901 (2018) 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.

Simulation of the quantum dynamics of indistinguishable bosons with the method of coupled coherent states

“…Further developments of the method that we envisage in future include development of methods to generate initial conditions, as imaginary time propagation is unstable with trajectories; incorporation of SU(n) coherent states, as demonstrated in Ref. [83]; and the combination of the method with one to treat identical fermions [84] to study Bose-Fermi mixtures, as has been carried out by MCTDH [85] and ML-MCTDH [86] previously.…”