Rotation Symmetry-Protected Topological Phases of Fermions

Abstract

We study classification of interacting fermionic symmetry-protected topological (SPT) phases with both rotation symmetry and Abelian internal symmetries in one, two, and three dimensions. By working out this classification, on the one hand, we demonstrate the recently proposed correspondence principle between crystalline topological phases and those with internal symmetries through explicit block-state constructions. We find that for the precise correspondence to hold it is necessary to change the central extension structure of the symmetry group by the ${\mathbb{Z}}_2$ fermion parity. On the other hand, we uncover new classes of intrinsically fermionic SPT phases that are only enabled by interactions, both in 2D and 3D with four-fold rotation. Moreover, several new instances of Lieb-Schultz-Mattis-type theorems for Majorana-type fermionic SPTs are obtained and we discuss their interpretations from the perspective of bulk-boundary correspondence.

are welcome; v2 published version, with new results on the group structure of 3D FSPTs

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Cited by in corpus (21)

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• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Intrinsically Interacting Higher-Order Topological Superconductors
• Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Classification and construction of interacting fractonic higher-order topological phases
• Effective field theories of topological crystalline insulators and topological crystals
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• Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries
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• Many-body multipole index and bulk-boundary correspondence
• Classification of symmetry-enriched topological quantum spin liquids
• Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
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• Intertwined topological phases in TaAs2 nanowires with giant magnetoresistance and quantum coherent surface transport
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• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
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