Stochastic evaluation of second-order Dyson self-energies

Area of Science:

• Computational chemistry
• Quantum many-body theory

Background:

• Calculating molecular electronic properties like quasiparticle energies is computationally intensive.
• Existing methods for second-order perturbation corrections can suffer from numerical noise and instability.

Purpose of the Study:

• To develop a direct and robust stochastic method for evaluating second-order perturbation corrections to Dyson self-energies.
• To improve the accuracy and efficiency of computing correlated ionization potentials and electron affinities.

Main Methods:

• A stochastic approach utilizing Laplace transforms to reformulate self-energy calculations.
• Monte Carlo integration of 13-dimensional integrals, with 12-dimensional parts handled by efficient importance sampling.
• Application of the Metropolis algorithm with a novel, analytically integrable weight function to manage integrand singularities.

Main Results:

• Accurate reproduction of quasiparticle energies for small molecules within a few mEh of reference values using 10^8 Monte Carlo steps.
• Demonstration of linear-to-quadratic scaling in computational cost with system size, even for small molecules.
• The method successfully avoids calculating small differences between large, noisy quantities.

Conclusions:

• The proposed stochastic method offers a direct and numerically stable alternative for calculating molecular electronic properties.
• This approach shows promise for efficient and accurate computations in quantum many-body Green's function theory.
• The method's favorable scaling suggests applicability to larger molecular systems.