Feynman Diagrams as Computational Graphs
Pengcheng Hou Tao Wang Daniel Cerkoney Xiansheng Cai Zhiyi Li Youjin Deng Lei Wang Kun Chen
We propose a computational graph representation of high-order Feynman
diagrams in Quantum Field Theory (QFT), applicable to any combination of
spatial, temporal, momentum, and frequency domains. Utilizing the
Dyson-Schwinger and parquet equations, our approach effectively organizes these
diagrams into a fractal structure of tensor operations, significantly reducing
computational redundancy. This approach not only streamlines the evaluation of
complex diagrams but also facilitates an efficient implementation of the
field-theoretic renormalization scheme, crucial for enhancing perturbative QFT
calculations. Key to this advancement is the integration of Taylor-mode
automatic differentiation, a key technique employed in machine learning
packages to compute higher-order derivatives efficiently on computational
graphs. To operationalize these concepts, we develop a Feynman diagram compiler
that optimizes diagrams for various computational platforms, utilizing machine
learning frameworks. Demonstrating this methodology's effectiveness, we apply
it to the three-dimensional uniform electron gas problem, achieving
unprecedented accuracy in calculating the quasiparticle effective mass at metal
density. Our work demonstrates the synergy between QFT and machine learning,
establishing a new avenue for applying AI techniques to complex quantum
many-body problems.