In this work we consider general fermion systems in two spatial dimensions, both with and without charge conservation symmetry, which realize a nontrivial fermionic topological order with only Abelian anyons. We address the question of precisely how these quantum phases differ from their bosonic counterparts, both in terms of their edge physics and in the way one would identify them in numerics. As in previous works, we answer these questions by studying the theory obtained after gauging the global fermion parity symmetry, which turns out to have a special and simple structure. Using this structure, a minimal scheme is outlined for how to numerically identify a general Abelian fermionic topological order, without making use of fermion number conservation. Along the way, some subtleties of the momentum polarization technique are discussed. Regarding the edge physics, it is shown that the gauged theory can have a (bosonic) gapped boundary to the vacuum if and only if the ungauged fermion theory has a gapped boundary as well.

中文翻译：

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阿贝尔费米子拓扑序的数值识别和有隙边界

在这项工作中，我们考虑了具有和不具有电荷守恒对称性的两个空间维度的一般费米子系统，它们实现了仅具有阿贝尔任意子的非平凡费米子拓扑序。我们解决了这些量子相位与它们的玻色子对应物有何不同的问题，无论是在边缘物理学方面，还是在人们用数字识别它们的方式方面。与之前的工作一样，我们通过研究测量全局费米子奇偶对称性后获得的理论来回答这些问题，结果证明它具有特殊而简单的结构。使用这种结构，概述了如何在不使用费米数守恒的情况下数字识别一般阿贝尔费米子拓扑序的最小方案。在此过程中，讨论了动量极化技术的一些微妙之处。