Symmetry Protected Topological States of Interacting Fermions and Bosons

Abstract

We study the classification of interacting fermionic and bosonic symmetry protected topological (SPT) states. We define a SPT state as whether or not it is separated from the trivial state through a bulk phase transition, which is a general definition applicable to SPT states with or without spatial symmetries. We show that in all dimensions short range interactions can reduce the classification of free fermion SPT states, and we demonstrate these results by making connection between fermionic and bosonic SPT states. We first demonstrate that our formalism gives the correct classification for all the known SPT states, with or without interaction, then we will generalize our method to SPT states that involve the spatial inversion symmetry.

19 pages, 3 figures

References in corpus (10)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Insulators with Inversion Symmetry
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Crystalline Insulators
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• The space group classification of topological band insulators
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect

Cited by in corpus (34)

• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Construction of bosonic symmetry-protected-trivial states and their topological invariants via $G\times SO(\infty )$ non-linear $\sigma$-models
• Global Anomalies on the Hilbert Space
• Symmetric Mass Generation
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Symmetry protected topological phases under decoherence
• Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model
• Topological Paramagnetism in Frustrated Spin-One Mott Insulators
• Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids
• Bridging Fermionic and Bosonic Short Range Entangled States
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• Fate of exceptional points under interactions: Reduction of topological classifications
• Complete phase diagram and topological properties of interacting bosons in one-dimensional superlattices
• Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions
• Bosonic Short Range Entangled states Beyond Group Cohomology classification
• Polaron in a $p+ip$ Fermi topological superfluid
• Definition and Classification of Fermi Surface Anomalies
• Symmetry-protected topological phases in the SU(N) Heisenberg spin chain: a Majorana-fermion approach
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals
• Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
• Interacting topological phases in thin films of topological mirror Kondo insulators
• Weakly interacting one-dimensional topological insulators: a bosonization approach
• Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries
• Reduction of $\mathbb{Z}$ classification of a two-dimensional weak topological insulator - real-space DMFT study -
• Fermionic symmetry-protected topological state in strained graphene
• Stacking Group Structure of Fermionic Symmetry-Protected Topological Phases
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Quantum Restored Symmetry Protected Topological Phases
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Perturbative and global anomalies in bosonic analogues of integer quantum Hall and topological insulator phases
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• Correspondence of topological classification between quantum graph extra dimension and topological matter