Determinant Monte Carlo algorithms for dynamical quantities in fermionic systems

TL;DR

This paper introduces three Monte Carlo determinantal algorithms for calculating dynamical properties of fermionic systems, demonstrating improved efficiency and accuracy over existing methods in the thermodynamic limit.

Contribution

The paper presents a novel recursive determinant-based Monte Carlo algorithm that outperforms previous methods in computing dynamical quantities for fermionic systems.

Findings

Higher perturbation orders achieved

Greater accuracy with same computational effort

Efficient recursive determinant approach

Abstract

We introduce and compare three different Monte Carlo determinantal algorithms that allow one to compute dynamical quantities, such as the self-energy, of fermionic systems in their thermodynamic limit. We show that the most efficient approach expresses the sum of a factorial number of one-particle-irreducible diagrams as a recursive sum of determinants with exponential complexity. By comparing results for the two-dimensional Hubbard model with those obtained from state-of-the-art diagrammatic Monte Carlo, we show that we can reach higher perturbation orders and greater accuracy for the same computational effort.