Time-reversal symmetric hierarchy of fractional incompressible liquids

Abstract

We provide an effective description of fractional topological insulators that include the fractional quantum spin Hall effect by considering the time-reversal symmetric pendant to the topological quantum field theories that encode the Abelian fractional quantum Hall liquids. We explain the hierarchical construction of such a theory and establish for it a bulk-edge correspondence by deriving the equivalent edge theory for chiral bosonic fields. Further, we compute the Fermi-Bose correlation functions of the edge theory and provide representative ground state wave functions for systems described by the bulk theory.

14 pages

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• Boson topological insulators: A window into highly entangled quantum phases
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Zoology of Fractional Chern Insulators
• Classification and analysis of two dimensional abelian fractional topological insulators
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• From the adiabatic theorem of quantum mechanics to topological states of matter
• Fractional (Chern and topological) insulators
• Time-reversal symmetric U(1) quantum spin liquids
• Effective field theories for topological insulators by functional bosonization
• A K matrix Construction of Symmetry Enriched Phases of Matter
• Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
• Higher Dimensional Quantum Hall Effect as A-Class Topological Insulator
• Topological phases in two-dimensional arrays of parafermionic zero modes
• CPT theorem and classification of topological insulators and superconductors
• Observation of the dual quantum spin Hall insulator by density-tuned correlations in a van der Waals monolayer
• Time reversal symmetry broken fractional topological phases at zero magnetic field
• Non-Abelian BF theory for 2+1 dimensional topological states of matter
• Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids
• Symmetry enriched U(1) quantum spin liquids
• D-Algebra Structure of Topological Insulators
• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• Duality and Dimensional Reduction of 5D BF Theory
• Fractional Chern Insulators in Twisted Bilayer MoTe${}_2$: A Composite Fermion Perspective
• Global phase diagram of two-component Bose gases in antiparallel magnetic fields
• Partition Functions and Stability Criteria of Topological Insulators
• Probing fractional topological insulators with magnetic edge perturbations
• Fractional topological insulators of Cooper pairs induced by proximity effect
• Higgsless superconductivity from topological defects in compact BF terms
• Interaction Protected Topological Insulators with Time Reversal Symmetry
• Time-Reversal Invariant Topological Moiré Flatband: A Platform for the Fractional Quantum Spin Hall Effect
• Interacting and fractional topological insulators via the ${\mathbb{Z}}_2$ chiral anomaly
• Transport via double constrictions in integer and fractional topological insulators
• The BF theory as an electric Julia-Toulouse condensate
• Topological BF theory of the quantum hydrodynamics of incompressible polar fluids
• Accessing topological order in fractionalized liquids with gapped edges
• Parafermions in Hierarchical Fractional Quantum Hall States
• Effective theory of fractional topological insulators in two spatial dimensions
• Fractional topological insulator precursors in spin-orbit fermion ladders
• Topological quantum criticality from multiplicative topological phases
• A Passage to Topological Matter: Colloquium
• Charge and spin fractionalization in strongly correlated topological insulators
• Pairing instabilities in topological insulator quantum wells
• Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe${}_2$ bilayers
• Spin separation due to an inherent spontaneous symmetry breaking of the fractional topological insulator
• The Weyl-Mott point: topological and non-Fermi liquid behavior from an isolated Green's function zero
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• The dynamics on the three-dimensional boundary of the 4D Topological BF model