Counting Feynman diagrams via many-body relations

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory
• Computational Physics

Background:

• Feynman diagrams are crucial for solving quantum many-body problems.
• Counting these diagrams, especially for exact solutions, is computationally challenging.
• Existing methods may struggle with complex interactions and approximations.

Purpose of the Study:

• To develop an efficient iterative algorithm for counting Feynman diagrams.
• To apply the algorithm to general fermionic many-body systems and specific approximations.
• To analyze low-order results and asymptotic behaviors of various functions.

Main Methods:

• An iterative algorithm based on many-body relations is presented.
• The algorithm is applied to parquet-type approximations.
• Spin-resolved diagrams in the Hubbard model are considered.

Main Results:

• The algorithm successfully counts Feynman diagrams at each order for exact solutions.
• It is effective for different parquet approximations and the Hubbard model.
• Low-order results and asymptotics for vertex functions and two-particle channels are discussed.

Conclusions:

• The developed algorithm provides an efficient way to count Feynman diagrams.
• It is versatile and can be generalized to various many-body relations and approximations.
• This method facilitates deeper analysis of quantum many-body systems.