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

Area of Science:

• Quantum Chemistry
• Computational Physics
• Many-Body Theory

Background:

• Zombie states provide a novel formalism for coupled coherent fermionic states.
• This approach aims to overcome the computational challenges posed by the fermionic sign problem.
• Prior work demonstrated Zombie states' adherence to fermionic algebra and their utility in real-time evolution.

Purpose of the Study:

• To develop efficient algorithms for Hamiltonian and operator evaluation within the Zombie state formalism.
• To address the normalization of Zombie states and enable accurate ground and excited state calculations.
• To introduce methods for improving computational efficiency and accuracy, such as biasing and wave function cleaning.

Main Methods:

• Development of efficient algorithms for evaluating operators between Zombie states.
• Implementation of imaginary time propagation for ground state determination.
• Introduction of a biasing method for constructing efficient random Zombie state basis sets.
• Application of wave function cleaning to remove erroneous electron configurations.
• Utilizing Gram-Schmidt orthogonalization for efficient excited state calculations.

Main Results:

• Efficient algorithms for Hamiltonian and operator evaluation in Zombie state formalism were developed.
• Imaginary time propagation successfully determined system ground states.
• A biasing method significantly reduced basis set size while maintaining accuracy.
• Wave function cleaning enhanced the precision of electronic structure calculations.
• Low-lying excited states were computed efficiently via Gram-Schmidt orthogonalization.

Conclusions:

• The extended Zombie state formalism offers efficient and accurate methods for fermionic system simulations.
• Imaginary time propagation on biased random Zombie state grids presents a viable alternative to quantum Monte Carlo methods.
• The developed techniques enhance the computational tractability and accuracy of simulating complex fermionic systems.