Electronic energies from coupled fermionic 'Zombie' states imaginary time evolution

TL;DR

This paper introduces an advanced formalism using Zombie States for fermionic systems, enabling efficient imaginary time evolution to find ground states and excited states, potentially offering an alternative to Quantum Monte Carlo methods.

Contribution

It develops algorithms for Hamiltonian evaluation, normalization, and wave function cleaning within the Zombie States formalism, extending its application to imaginary time evolution.

Findings

Efficient algorithms for Hamiltonian and operator evaluation between Zombie States.

Successful imaginary time propagation to find electronic ground states.

Wave function cleaning improves accuracy and reduces basis size.

Abstract

Zombie States are a recently introduced formalism to describe coupled coherent Fermionic states which address the Fermionic sign problem in a computationally tractable manner. Previously it has been shown that Zombie States with fractional occupations of spin-orbitals obeyed the correct Fermionic creation and annihilation algebra and presented results for real-time evolution [Dmitrii V. Shalashilin, J. Chem. Phys. 148, 194109 (2018)]. In this work we extend and build on this formalism by developing efficient algorithms for evaluating the Hamiltonian and other operators between Zombie States and address their normalization. We also show how imaginary time propagation can be used to find the ground state of a system. We also present a biasing method, for setting up a basis set of random Zombie States, that allow much smaller basis sizes to be used while still accurately describing the electronic structure Hamiltonian and its ground state and describe a technique of wave function "cleaning" which removes the contributions of configurations with the wrong number of electrons, improving the accuracy further. We also show how low-lying excited states can be calculated efficiently using a Gram-Schmidt orthogonalization procedure.The proposed algorithm of imaginary time propagation on a biased random grids of Zombie States may present an alternative to existing Quantum Monte Carlo methods.