Monte Carlo Second- and Third-Order Many-Body Green's Function Methods with Frequency-Dependent, Nondiagonal...

Area of Science:

• Computational Chemistry
• Quantum Many-Body Theory
• Electronic Structure Theory

Background:

• The Monte Carlo many-body Green's function (MC-GF) method is a powerful tool for electronic structure calculations.
• Previous implementations were limited by lower-order perturbation expansions and computational bottlenecks.
• Accurate calculation of electron binding energies is crucial for understanding molecular properties.

Purpose of the Study:

• To fully develop and enhance the MC-GF method for greater accuracy and efficiency.
• To investigate the impact of third-order perturbation corrections on electronic properties.
• To establish guidelines for optimal computational resource allocation in MC-GF calculations.

Main Methods:

• Implemented a third-order perturbation expansion (MC-GF3) using a computerized enumeration of Goldstone diagrams.
• Developed an efficient algorithm for computing self-energy matrices via common subexpression elimination.
• Introduced stochastic integration for imaginary-time calculations, achieving significant speedups (50-200x).
• Analyzed the redundant-walker convergence scheme to optimize walker selection for constant cost per sample.

Main Results:

• Achieved a significant speedup in calculations through stochastic integration and efficient algorithms.
• Demonstrated that third-order corrections are substantial for electron binding energies, impacting convergence.
• Observed a favorable scaling of computational cost with molecular size (O(n^4)-O(n^5)) compared to deterministic methods (O(n^5)-O(n^6)).

Conclusions:

• The developed MC-GF3 method offers a computationally efficient and accurate approach for electronic structure.
• Third-order perturbation corrections are essential for accurate electron binding energies, showing oscillatory convergence.
• The findings justify the use of MC-GF3 and motivate the development of even higher-order methods.