Recently, it has been found that there exist symmetry-protected topological phases of fermions, which have no realizations in non-interacting fermionic systems or bosonic models. We study the edge states of such an intrinsically interacting fermionic SPT phase in two spatial dimensions, protected by $\mathbb{Z}_4\times\mathbb{Z}_2^T$ symmetry. We model the edge Hilbert space by replacing the internal $\mathbb{Z}_4$ symmetry with a spatial translation symmetry, and design an exactly solvable Hamiltonian for the edge model. We show that at low-energy the edge can be described by a two-component Luttinger liquid, with nontrivial symmetry transformations that can only be realized in strongly interacting systems. We further demonstrate the symmetry-protected gaplessness under various perturbations, and the bulk-edge correspondence in the theory.

中文翻译：

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二维费米子对称保护拓扑相的相互作用边缘态

近来，已经发现存在费米子的对称保护的拓扑相，这在非相互作用的费米离子系统或玻色子模型中没有实现。我们在两个空间维度上研究了这种内在相互作用的铁离子SPT相的边缘状态，并受到$ \ mathbb {Z} _4 \ times \ mathbb {Z} _2 ^ T $对称性的保护。我们通过将内部$ \ mathbb {Z} _4 $对称性替换为空间平移对称性来对边缘希尔伯特空间建模，并为边缘模型设计一个完全可解的哈密顿量。我们表明，在低能状态下，边缘可以由两组分的Luttinger液体描述，具有非平凡的对称变换，只能在强相互作用的系统中实现。我们进一步证明了在各种扰动下对称保护的无间隙性以及理论中的体边缘对应性。