Determinant Diagrammatic Monte Carlo Algorithm in the Thermodynamic Limit.

Area of Science:

• Quantum many-body physics
• Computational condensed matter physics

Background:

• Feynman diagrams are crucial for understanding fermionic models.
• Conventional diagrammatic Monte Carlo algorithms face challenges with sign problems and computational complexity.
• Analytical calculations in the thermodynamic limit are often difficult.

Purpose of the Study:

• To present a simplified and more efficient method for summing connected Feynman diagrams.
• To enable analytical calculations in the thermodynamic limit for general fermionic models.
• To overcome the sign problem inherent in diagrammatic techniques.

Main Methods:

• A novel trick to sum all connected Feynman diagrams at fixed vertex positions.
• Analytical treatment of the thermodynamic limit.
• Leveraging massive cancellations between diagrams to mitigate the sign problem.

Main Results:

• Achieved superior performance compared to conventional diagrammatic Monte Carlo algorithms.
• Demonstrated a dramatic simplification of the algorithmic process.
• Computational effort scales exponentially with expansion order, unlike the factorial growth of standard methods.
• Successfully illustrated the technique's efficiency on the two-dimensional Fermi-Hubbard model.

Conclusions:

• The presented method offers a significant advancement in the computational study of fermionic systems.
• This approach simplifies complex calculations and enhances efficiency, particularly for models like the Fermi-Hubbard model.
• The technique effectively reduces the sign problem, paving the way for more tractable analytical solutions.