The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry

Abstract

We study the effect of interactions on 2D fermionic symmetry-protected topological (SPT) phases using the recently proposed braiding statistics approach. We focus on a simple class of examples: superconductors with a Z2 Ising symmetry. Although these systems are classified by Z in the noninteracting limit, our results suggest that the classification collapses to Z8 in the presence of interactions -- consistent with previous work that analyzed the stability of the edge. Specifically, we show that there are at least 8 different types of Ising superconductors that cannot be adiabatically connected to one another, even in the presence of strong interactions. In addition, we prove that each of the 7 nontrivial superconductors have protected edge modes.

5 pages, 1 figure

References in corpus (2)

• Classification of topological insulators and superconductors in three spatial dimensions
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect

Cited by in corpus (121)

• Classification of topological quantum matter with symmetries
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Topological Superconductivity in Twisted Multilayer Graphene
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Classification of interacting electronic topological insulators in three dimensions
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Topological phases protected by point group symmetry
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Topological superconductivity in Dirac semimetals
• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Spin TQFTs and fermionic phases of matter
• Observation of symmetry-protected topological band with ultracold fermions
• State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
• Gapless Symmetry Protected Topological Order
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Symmetry Protected Topological phases and Generalized Cohomology
• Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
• Topological Transition on the Conformal Manifold
• Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
• Theory of interacting topological crystalline insulators
• Topological invariants for gauge theories and symmetry-protected topological phases
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• Many-body topological invariants for fermionic symmetry-protected topological phases
• Topological Luttinger Liquids from Decorated Domain Walls
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• Many-body localization, symmetry, and topology
• Global Anomalies on the Hilbert Space
• Discrete Theta Angles, Symmetries and Anomalies
• Exotic Quantum Phase Transitions of $(2+1)d$ Dirac fermions
• Symmetric Mass Generation
• Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Classification of 2+1D topological orders and SPT orders for bosonic and fermionic systems with on-site symmetries
• Symmetric Fermion Mass Generation as Deconfined Quantum Criticality
• Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
• Construction and classification of symmetry protected topological phases in interacting fermion systems
• Composite Dirac liquids: parent states for symmetric surface topological order
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Classification of (2+1)D invertible fermionic topological phases with symmetry
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Discrete spin structures and commuting projector models for 2d fermionic symmetry protected topological phases
• Interacting fermionic symmetry-protected topological phases in two dimensions
• Symmetry protected topological phases under decoherence
• Bona fide interaction-driven topological phase transition in correlated SPT states
• Duality and bosonization of (2+1)d Majorana fermions
• Fermionic projected entangled-pair states and topological phases
• Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions
• Multi-kink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF theory
• Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model
• Decorated ${\mathbb{Z}}_2$ Symmetry Defects and Their Time-Reversal Anomalies
• Dimensional Reduction and Topological Invariants of Symmetry-Protected Topological Phases
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• Lorentz Symmetry Fractionalization and Dualities in (2+1)d
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification
• Topological invariants for interacting topological insulators: II. Breakdown of the Green's function formalism
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Quantum Monte Carlo study of strange correlator in interacting topological insulators
• Bridging Fermionic and Bosonic Short Range Entangled States
• Construction and classification of point group symmetry protected topological phases in 2D interacting fermionic systems
• Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking
• Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
• Topological number and Fermion Green's function of Strongly Interacting Topological Superconductors
• Correlation effects on topological crystalline insulators
• Fermion decoration construction of symmetry protected trivial orders for fermion systems with any symmetries $G_f$ and in any dimensions
• Dimensional hierarchy of fermionic interacting topological phases
• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
• `Gauging' time reversal symmetry in tensor network states
• Braiding statistics and classification of two-dimensional charge-$2m$ superconductors
• Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way
• Disentangling interacting symmetry protected phases of fermions in two dimensions
• Fermi Surface Symmetric Mass Generation
• Intrinsically Interacting Higher-Order Topological Superconductors
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Bosonic Short Range Entangled states Beyond Group Cohomology classification
• Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
• Spin-cobordisms, surgeries and fermionic modular bootstrap
• Classification and construction of interacting fractonic higher-order topological phases
• Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study
• Generic "Unnecessary" Quantum Critical Points with Minimal Degrees of Freedom
• Interacting topological mirror excitonic insulator in one dimension
• Definition and Classification of Fermi Surface Anomalies
• Criteria for protected edge modes with ${\mathbb{Z}}_2$ symmetry
• Quantum phase transitions of topological insulators without gap closing
• Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries
• Extracting topological orders of generalized Pauli stabilizer codes in two dimensions
• Interacting Topological Insulators with Synthetic Dimensions
• Topological Charge/spin density Wave in InAs/GaSb Quantum Wells under an In-plane Magnetic Field
• Interacting Valley Chern Insulator and its Topological Imprint on Moiré Superconductors
• Dynamical bulk-edge correspondence for nodal lines in parameter space
• Edge theories of 2D fermionic symmetry protected topological phases protected by unitary Abelian symmetries
• Topological phases of parafermionic chains with symmetries
• Spontaneous Symmetry Breaking and Phase Coexistence in Two-Color Networks
• A no-go result for implementing chiral symmetries by locality-preserving unitaries in a 3 dimensional Hamiltonian lattice model of fermions
• Commuting-projector Hamiltonians for chiral topological phases built from parafermions
• Non-Abelian Three-Loop Braiding Statistics for 3D Fermionic Topological Phases
• Duality Defect of the Monster CFT
• Generalized toric codes on twisted tori for quantum error correction
• Trialities of minimally supersymmetric 2d gauge theories
• LSM and CPT
• Exactly solvable lattice models for interacting electronic insulators in two dimensions
• Characterization and Classification of Fermionic Symmetry Enriched Topological Phases
• Mirror anomaly in fermionic topological orders
• Interacting topological phases in thin films of topological mirror Kondo insulators
• Stability of Topological Insulators with Non-Abelian Edge Excitations
• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• A search for correlation-induced adiabatic paths between distinct topological insulators
• Stacking Group Structure of Fermionic Symmetry-Protected Topological Phases
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices
• SPT extension of $Z_2$ quantum Ising model's ferromagnetic phase
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• (2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes
• Combined spontaneous symmetry-breaking and symmetry-protected topological order from cluster charge interaction