Construction and classification of point group symmetry protected topological phases in 2D interacting fermionic systems

Abstract

The construction and classification of symmetry-protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Very recently, a complete classification and construction of space group SPT phases were also proposed for interacting bosonic systems. In this paper, we attempt to generalize this classification and construction scheme systematically into interacting fermion systems. In particular, we construct and classify point group SPT phases for 2D interacting fermion systems via lower-dimensional block-state decorations. We discover several intriguing fermionic SPT states that can only be realized in interacting fermion systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for 2D interacting fermion systems. Finally, the potential experimental realization of these new classes of point group SPT phases in 2D correlated superconductors is addressed.

arXiv comment4+epsilon pages, 4 figures, 2 tables; with supplementary material; Published version

References in corpus (41)

• Topological Insulators
• Topological insulators and superconductors
• Unpaired Majorana fermions in quantum wires
• Topological Crystalline Insulators
• High-temperature superconductivity in iron-based materials
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Superconductivity in single-layer films of FeSe with a transition temperature above 100 K
• Experimental realization of a topological crystalline insulator in SnTe
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Topological phases of fermions in one dimension
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• Phase Diagram and High Temperature Superconductivity at 65 K in Tuning Carrier Concentration of Single-Layer FeSe Films
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Interface-induced superconductivity and strain-dependent spin density wave in FeSe/SrTiO3 thin films
• The space group classification of topological band insulators
• Braiding statistics approach to symmetry-protected topological phases
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Three-dimensional topological photonic crystal with a single surface Dirac cone
• Observation of Dirac node formation and mass acquisition in a topological crystalline insulator
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Topological phases protected by point group symmetry
• Building crystalline topological phases from lower-dimensional states
• Gauging spatial symmetries and the classification of topological crystalline phases
• Higher Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures
• Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSb
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• Theory of interacting topological crystalline insulators
• Topological states from topological crystals
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• Crystalline topological phases as defect networks
• Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
• Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions
• Interacting fermionic symmetry-protected topological phases in two dimensions
• Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions
• Dimensional Reduction and Topological Invariants of Symmetry-Protected Topological Phases
• Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids
• Short-Range Entangled Bosonic States with Chiral Edge Modes and $T$-duality of Heterotic Strings

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