Classification and analysis of two dimensional abelian fractional topological insulators

Abstract

We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have abelian braiding statistics. First, we construct the most general Chern-Simons theories that can describe these states. We then derive a criterion for when these systems have protected gapless edge modes -- that is, edge modes that cannot be gapped out without breaking time reversal or charge conservation symmetry. The systems with protected edge modes can be regarded as fractionalized analogues of topological insulators. We show that previous examples of 2D fractional topological insulators are special cases of this general construction. As part of our derivation, we define the concept of "local Kramers degeneracy" and prove a local version of Kramers theorem.

19 pages, 2 figures, added reference, corrected typos

References in corpus (3)

• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Fractional topological insulators in three dimensions
• Improved position measurement of nano electromechanical systems using cross correlations

Cited by in corpus (160)

• Classification of topological quantum matter with symmetries
• Symmetry Protected Topological phases of Quantum Matter
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• A classification of symmetry enriched topological phases with exactly solvable models
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Boson topological insulators: A window into highly entangled quantum phases
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Protected edge modes without symmetry
• Symmetry protected topological phases from decorated domain walls
• Integer quantum Hall effect for bosons: A physical realization
• Correlation effects in two-dimensional topological insulators
• Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States
• Subsystem symmetry protected topological order
• Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
• Superconductivity from Valley Fluctuations and Approximate SO(4) Symmetry in a Weak Coupling Theory of Twisted Bilayer Graphene
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• Anomalous Symmetry Fractionalization and Surface Topological Order
• Gapless Symmetry Protected Topological Order
• Exactly Solvable Models for Symmetry-Enriched Topological Phases
• Emergent Phases of Fractonic Matter
• Symmetry constraints on many-body localization
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids
• Wave Functions of Bosonic Symmetry Protected Topological Phases
• Higher-order Topological Mott Insulators
• Cage-Net Fracton Models
• Symmetric Fracton Matter: Twisted and Enriched
• Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies
• Symmetry-Enriched Quantum Spin Liquids in $(3+1)d$
• Fractional (Chern and topological) insulators
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Spontaneous breakdown of topological protection in two dimensions
• Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent $QE{D}_3$ and anyon superfluid
• Time-reversal symmetric U(1) quantum spin liquids
• Constraints on topological order in Mott Insulators
• Twisted Injectivity in PEPS and the Classification of Quantum Phases
• Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions
• Fractional Topological Insulators -- a Pedagogical Review
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Chiral-symmetry protected exceptional torus in correlated nodal-line semi-metals
• Anomaly indicators for time-reversal symmetric topological orders
• Effective field theories for topological insulators by functional bosonization
• Bulk-boundary correspondence for three-dimensional symmetry-protected topological phases
• A K matrix Construction of Symmetry Enriched Phases of Matter
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Topological phases in layered pyrochlore oxide thin films along the [111] direction
• Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
• Multi-kink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF theory
• Universal Quantum Computation with Gapped Boundaries
• Exceptional band touching for strongly correlated systems in equilibrium
• Spectroscopic signatures of crystal momentum fractionalization
• Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter
• Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory
• Lattice distortion effects on topological phases in (LaNiO${}_3$)${}_2$/(LaAlO${}_3$)${}_N$ heterostructures grown along the [111] direction
• Topological phases in two-dimensional arrays of parafermionic zero modes
• ${\mathbb{Z}}_2$ fractional topological insulators in two dimensions
• CPT theorem and classification of topological insulators and superconductors
• Exact realization of Integer and Fractional Quantum Hall Phases in U(1)xU(1) models in (2+1)d
• Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations
• Weak symmetry breaking in two dimensional topological insulators
• Detection of Symmetry Enriched Topological Phases
• Time reversal symmetry broken fractional topological phases at zero magnetic field
• Chiral spin density wave, spin-charge-Chern liquid and d+id superconductivity in 1/4-doped correlated electronic systems on the honeycomb lattice
• Quantum Field Theory Anomalies in Condensed Matter Physics
• Symmetry enriched U(1) quantum spin liquids
• Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids
• Symmetry Enrichment in Three-Dimensional Topological Phases
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification
• Resonant Raman scattering theory for Kitaev models and their Majorana fermion boundary modes
• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• Three Dimensional Z2 Topological Phases enriched by Time-Reversal Symmetry
• Lattice model constructions for gapless domain walls between topological phases
• Correlation effects on topological crystalline insulators
• Symmetry fractionalization and anomaly detection in three-dimensional topological phases
• Globally symmetric topological phase: from anyonic symmetry to twist defect
• Fate of Majorana modes in ${\mathrm{CeCoIn}}_5$/${\mathrm{YbCoIn}}_5$ superlattices -a test bed for reduction of topological classification-
• Microscopic Theory of Surface Topological Order for Topological Crystalline Superconductors
• Unquantized anomalies in topological semimetals
• Parafermionic wires at the interface of chiral topological states
• Gapped symmetric edges of symmetry protected topological phases
• String flux mechanism for fractionalization in topologically ordered phases
• Space group symmetry fractionalization in a family of exactly solvable models with Z2 topological order
• Relative Anomaly in (1+1)d Rational Conformal Field Theory
• Fate of exceptional points under interactions: Reduction of topological classifications
• Two dimensional Symmetry Protected Topological Phases with PSU(N) and time reversal symmetry
• `Gauging' time reversal symmetry in tensor network states
• Braiding statistics and classification of two-dimensional charge-$2m$ superconductors
• Topological Phases on Non-orientable Surfaces: Twisting by Parity Symmetry
• Anyon Condensation: Coherent states, Symmetry Enriched Topological Phases, Goldstone Theorem, and Dynamical Rearrangement of Symmetry
• Reduction of topological $\mathbb{Z}$ classification in cold atomic systems
• Folding approach to topological orders enriched by mirror symmetry
• Global phase diagram of two-component Bose gases in antiparallel magnetic fields
• Partition Functions and Stability Criteria of Topological Insulators
• Bosonic symmetry protected topological phases with reflection symmetry
• Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces
• Supersymmetry "protected" topological phases of isostatic lattices and kagome antiferromagnets
• Phase diagram of two interacting helical states
• Anomaly indicators for topological orders with $U(1)$ and time-reversal symmetry
• Surface field theories of point group symmetry protected topological phases
• Line defects in Three dimensional Symmetry Protected Topological Phases
• Interaction Protected Topological Insulators with Time Reversal Symmetry
• Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
• Families of Gapped Interfaces Between Fractional Quantum Hall States
• Fractonic topological phases from coupled wires
• Interacting and fractional topological insulators via the ${\mathbb{Z}}_2$ chiral anomaly
• Criteria for protected edge modes with ${\mathbb{Z}}_2$ symmetry
• Classification and surface anomaly of glide symmetry protected topological phases in three dimensions
• Three-dimensional Topological Insulators and Bosonization
• Stability of a topological insulator: interactions, disorder and parity of Kramers doublets
• Transport via double constrictions in integer and fractional topological insulators
• Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries
• Minimal Fractional Topological Insulator in half-filled conjugate moiré Chern bands
• Symmetry-induced anyon "breeding" in fractional quantum Hall states
• Edge theories of 2D fermionic symmetry protected topological phases protected by unitary Abelian symmetries
• Topological phases of parafermionic chains with symmetries
• Composite helical edges from Abelian fractional topological insulators
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Fractional quantum Hall effect in a relativistic field theory
• Interacting Edge States of Fermionic Symmetry-Protected Topological Phases in Two Dimensions
• Accessing topological order in fractionalized liquids with gapped edges
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases
• Effective theory of fractional topological insulators in two spatial dimensions
• Parafermions in Hierarchical Fractional Quantum Hall States
• Textured Exciton Insulators
• Rotational Symmetry Protected Edge and Corner States in Abelian topological phases
• Topological Modes Protected by Chiral and Two-Fold Rotational Symmetry in a Spring-Mass Model with a Lieb Lattice Structure
• Current enhancement through a time dependent constriction in fractional topological insulators
• Universal Wilson Loop Bound of Quantum Geometry
• Edge--Entanglement correspondence for gapped topological phases with symmetry
• Topological quantum criticality from multiplicative topological phases
• A Passage to Topological Matter: Colloquium
• $U(1)$ symmetry-enriched toric code
• Chern insulator transitions with Wilson fermions on a hyperrectangular lattice
• Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator
• Time reversal invariant gapped boundaries of the double semion state
• Stability of Topological Insulators with Non-Abelian Edge Excitations
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases II: The (2+1)-Dimensional Case
• Characterization and Classification of Fermionic Symmetry Enriched Topological Phases
• Perturbative BF theory
• Topological properties of magnetically ordered heavy-fermion systems in the presence of mirror symmetry
• Bound states of three fermions forming symmetry-protected topological phases
• Gauging Defects in Quantum Spin Systems
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• A Recipe for Constructing Frustration-Free Hamiltonians with Gauge and Matter Fields in One and Two Dimensions
• Reduction of $\mathbb{Z}$ classification of a two-dimensional weak topological insulator - real-space DMFT study -
• Candidate for a Fractional Topological Insulator in Twisted MoTe2
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Variational wavefunctions for fractional topological insulators
• Symmetry-protected gates of Majorana qubits in a high-$T_c$ superconductor platform
• Periodic dynamics in an Ising chain with a quadratic transverse field
• Tuning between a fractional topological insulator and competing phases at ${\nu }_{\mathrm{T}}=2/3$
• Symmetric localization of ${\nu }_{\text{tot}}=4/3$ fractional topological insulator edges