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Combinatorial summation of Feynman diagrams
1Department of Physics, King's College London, London, UK. evgeny.kozik@kcl.ac.uk.
Nature Communications
|September 10, 2024
Summary
This study introduces a new framework for efficiently summing Feynman diagrams in quantum many-body systems. This method aids in precise computational techniques and offers potential advantages for quantum computing applications.
Area of Science:
- Quantum Many-Body Physics
- Computational Physics
- Quantum Computing
Background:
- Feynman's diagrammatic series is crucial for describing interacting quantum particles.
- Existing methods face challenges in computational complexity for complex systems.
Purpose of the Study:
- To develop a universal framework for efficient summation of Feynman diagrams.
- To enable precise computational techniques for quantum many-body systems.
Main Methods:
- Introduced a combinatorial construction for summing Feynman diagram integrands.
- Utilized dynamic programming for efficient summation.
- Applied diagrammatic Monte Carlo for calculations.
Main Results:
- Developed a framework with computational cost exponential in diagram order (classical) or polynomial (quantum).
- Successfully calculated the equation of state for the 2D SU(N) Hubbard model.
- Addressed a problem challenging for current numerical methods.
Conclusions:
- The new framework offers efficient summation of Feynman diagrams for quantum many-body systems.
- This approach has potential for both classical and quantum computation.
- Demonstrated applicability to a challenging, experimentally relevant model system.
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