Efficient Quasiparticle Determination beyond the Diagonal Approximation via Random Compression

TL;DR

This paper introduces a stochastic method to accurately compute quasiparticle states beyond the diagonal approximation in large systems, significantly reducing computational complexity while maintaining accuracy.

Contribution

It extends stochastic approaches in many-body perturbation theory to go beyond the diagonal approximation, enabling efficient quasiparticle calculations in large systems.

Findings

Achieved up to 95% problem size compression using stochastic sampling.

Successfully computed hole injection energies into CO2 on a gold surface with nearly 3000 electrons.

Demonstrated the method's potential for self-consistent stochastic calculations and Dyson orbital determination.

Abstract

Calculations of excited states in Green's function formalism often invoke the diagonal approximation, in which the quasiparticle states are taken from a mean-field calculation. Here, we extend the stochastic approaches applied in the many-body perturbation theory and overcome this limitation for large systems in which we are interested in a small subset of states. We separate the problem into a core subspace, whose coupling to the remainder of the system environment is stochastically sampled. This method is exemplified on computing hole injection energies into CO$_2$ on an extended gold surface with nearly 3000 electrons. We find that in the extended system, the size of the problem can be compressed up to $95\%$ using stochastic sampling. This result provides a way forward for self-consistent stochastic methods and determining Dyson orbitals in large systems.