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

TL;DR

This paper explores the fermionic sign structure in high-order Feynman diagrams for a many-fermion system, revealing symmetry-based cancellations that enable a significantly faster Monte Carlo algorithm and inform effective field theory development.

Contribution

It systematically analyzes fermionic sign cancellations using symmetry arguments, leading to a highly efficient diagrammatic Monte Carlo method and insights for effective field theory construction.

Findings

Sign cancellations are governed by crossing and gauge symmetries.

The new Monte Carlo algorithm is about 10^5 times faster at sixth order.

Analysis provides guidance for constructing effective field theories.

Abstract

The sign cancellation between scattering amplitudes makes fermions different from bosons. We systematically investigate Feynman diagrams' fermionic sign structure in a representative many-fermion system---a uniform Fermi gas with Yukawa interaction. We analyze the role of the crossing symmetry and the global gauge symmetry in the fermionic sign cancellation. The symmetry arguments are then used to identify the sign-canceled groups of diagrams. Sign-structure analysis has two applications. Numerically, it leads to a cluster diagrammatic Monte 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 relevant effective field theory for many-fermion systems.