The classification and lattice model construction of symmetry-protected topological (SPT) phases in interacting fermion systems are very interesting but challenging. In this paper, we give a systematic fixed-point wave function construction of fermionic SPT (FSPT) states for generic fermionic symmetry group $G_f={\mathbb{Z}}_2^f{\times }_{{\omega }_2}{G}_b$ which is a central extension of bosonic symmetry group $G_b$ (may contain time-reversal symmetry) by the fermion parity symmetry group ${\mathbb{Z}}_2^f=\{1,P_f\}$. Our construction is based on the concept of an equivalence class of finite-depth fermionic symmetric local unitary transformations and decorating symmetry domain wall picture, subjected to certain obstructions. We also discuss the systematical construction and classification of boundary anomalous SPT states which leads to a trivialization of the corresponding bulk FSPT states. Thus, we conjecture that the obstruction-free and trivialization-free constructions naturally lead to a classification of FSPT phases. Each fixed-point wave function admits an exactly solvable commuting-projector Hamiltonian. We believe that our classification scheme can be generalized to point and space group symmetry as well as continuum Lie group symmetry.

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相互作用费米子系统中受对称保护的拓扑相的构造和分类

相互作用的费米子系统中对称保护拓扑（SPT）相的分类和晶格模型构造非常有趣，但具有挑战性。在本文中，我们为一般的铁离子对称群给出了系统的费米SPT（FSPT）态定点波函数构造$G_F={\mathbb{ž}}_2^F{\times }_{{\omega }_2}{G}_b$ 这是玻色子对称群的主要扩展 $G_b$ （可能包含时间反转对称）由费米子奇偶校验对称组 ${\mathbb{ž}}_2^F=\{\mathrm{1个}，P_F\}$。我们的构造基于有限深度的费米离子对称局部unit变换和装饰对称畴壁图片的等价类的概念，该图像受到某些障碍。我们还讨论了边界异常SPT状态的系统构建和分类，这导致了相应的大量FSPT状态的琐碎化。因此，我们推测无障碍和无琐事的构造自然会导致FSPT相的分类。每个定点波函数都允许一个完全可解的通勤投影仪哈密顿量。我们相信我们的分类方案可以推广到点和空间群对称性以及连续李群对称性。