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首页> 外文期刊>Physical Review X >Towards a Complete Classification of Symmetry-Protected Topological Phases for Interacting Fermions in Three Dimensions and a General Group Supercohomology Theory
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Towards a Complete Classification of Symmetry-Protected Topological Phases for Interacting Fermions in Three Dimensions and a General Group Supercohomology Theory

机译：朝着三维间隔互动的对称保护拓扑阶段的完整分类和一般组超级学理论

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摘要

The classification and construction of symmetry-protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that (generalized) group cohomology theory or cobordism theory gives rise to a complete classification of SPT phases in interacting boson or spin systems. The construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in three dimensions. In this work, we revisit this problem based on an equivalence class of fermionic symmetric local unitary transformations. We construct very general fixed-point SPT wave functions for interacting fermion systems. We naturally reproduce the partial classifications given by special group supercohomology theory, and we show that with an additional B ? H 2 ( G b , Z 2 ) structure [the so-called obstruction-free subgroup of H 2 ( G b , Z 2 ) ], a complete classification of SPT phases for three-dimensional interacting fermion systems with a total symmetry group G f = G b × Z 2 f can be obtained for unitary symmetry group G b . We also discuss the procedure for deriving a general group supercohomology theory in arbitrary dimensions.
机译：近年来，在糖镰和费米焦系统中相互作用的对称保护拓扑（SPT）阶段的分类和构建已成为令人着迷的理论方向。已经表明（广义）组同盟学理论或政府主义理论引发了甜糖或旋转系统中的SPT阶段的完整分类。互动米子系统中SPT阶段的结构和分类更加复杂，特别是三维。在这项工作中，我们根据Fermionic对称局部酉变换的等价类重新审视这个问题。我们构建了非常一般的定点SPT波函数，用于交互式费率系统。我们自然地再现了特殊群体超级学业理论给出的部分分类，我们展示了额外的B？ H 2（g b，z 2）结构[H 2（g b，z 2）的所谓的无阻塞子组]，具有总对称组g的三维相互作用的铁饼系统的SPT相的完整分类对于单一对称组G B可以获得F = G×Z 2 F.我们还讨论了在任意维度中导出总体超级学业理论的程序。

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