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The sign cancellation between scattering amplitudes makes fermions differentfrom bosons. We systematically investigate Feynman diagrams' fermionic signstructure in a representative many-fermion system---a uniform Fermi gas withYukawa interaction. We analyze the role of the crossing symmetry and the globalgauge symmetry in the fermionic sign cancellation. The symmetry arguments arethen used to identify the sign-canceled groups of diagrams. Sign-structureanalysis has two applications. Numerically, it leads to a cluster diagrammaticMonte Carlo algorithm for fast diagram evaluations. The new algorithm is about$10^5$ times faster than the conventional approaches in the sixth order.Furthermore, our analysis provides important hints in constructing the relevanteffective field theory for many-fermion systems.

Fermionic Sign Structure of High-order Feynman diagrams in a Many-fermion System