Fermionic sign structure of high-order Feynman diagrams in a many-fermion system
Fermionic sign structure of high-order Feynman diagrams in a many-fermion system
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DOI：
10.1103/physrevb.103.115141
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发表时间：
2020-10
影响因子：
3.7
通讯作者：
Bao-Zong Wang;Pengcheng Hou;Youjin Deng;K. Haule;Kun Chen
中科院分区：
文献类型：
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作者：
Bao-Zong Wang;Pengcheng Hou;Youjin Deng;K. Haule;Kun Chen
散射振幅之间的符号抵消使得费米子不同于玻色子。我们系统地研究了具有代表性的多费米子系统——具有汤川相互作用的均匀费米气体中的费曼图费米子符号结构。我们分析了交叉对称和全局规范对称在费米子符号消去中的作用。然后使用对称参数来识别消号图组。符号结构分析有两个应用。在数值上，它导致了一个聚类图蒙特卡罗算法快速图的评估。新算法比传统方法在六阶上快10^5美元。此外，我们的分析为构建多费米子系统的相关有效场论提供了重要的线索。
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.