Interaction Enabled Fractonic Higher-Order Topological Phases

Abstract

In this work, we present a collection of three-dimensional higher-order symmetry protected topological phases (HOSPTs) with gapless hinge modes that exist only in strongly interacting systems subject to subsystem symmetry constraints. We use a coupled wire construction to generate three families of microscopic lattice models: insulators with helical hinge modes, superconductors with chiral Majorana hinge modes, and fractionalized insulators with helical hinge modes that carry fractional charge. In particular, these HOSPTs do not require spatial symmetry protection, but are instead protected by subsystem symmetries, and support "fractonic" quasiparticle excitations that move within only a low-dimensional sub-manifold of the system. We analyze the anomaly structure for the boundary theory and the entanglement Hamiltonian, and show that the side surfaces of these HOSPTs, despite being partially gapped, exhibit symmetry anomalies, and can only be realized as the boundary of three-dimensional HOSPT phases.

arXiv comment16 pages, 9 figures

References in corpus (60)

• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Acoustic higher-order topological insulator on a Kagome lattice
• Zoo of quantum-topological phases of matter
• Higher-Order Topology in Bismuth
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Symmetry Protected Topological phases of Quantum Matter
• The effects of interactions on the topological classification of free fermion systems
• Topological protection of photonic mid-gap cavity modes
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Fractons
• Observation of second-order topological insulators in sonic crystals
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Fracton Phases of Matter
• From Luttinger liquid to non-Abelian quantum Hall states
• Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology
• Subsystem symmetry protected topological order
• Material design with the van der Waals stacking of bismuth-halide chains realizing a higher-order topological insulator
• Theta-terms in nonlinear sigma-models
• Foliated fracton order from gauging subsystem symmetries
• Dual gauge field theory of quantum liquid crystals in two dimensions
• Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
• Topological Quantum Glassiness
• How universal is the entanglement spectrum?
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Spin Charge Separation in the Quantum Spin Hall State
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Fractal Symmetric Phases of Matter
• Wave Functions of Bosonic Symmetry Protected Topological Phases
• Classification of subsystem symmetry-protected topological phases
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Symmetric Fracton Matter: Twisted and Enriched
• Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons
• Fracton fusion and statistics
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• A systematic construction of gapped non-liquid states
• Wire constructions of Abelian topological phases in three or more dimensions
• From an array of quantum wires to three-dimensional fractional topological insulators
• Fractional topological phases in three-dimensional coupled-wire systems
• Subsystem symmetry enriched topological order in three dimensions
• Dynamical Generation of Topological Masses in Dirac Fermions
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Fermion masses without symmetry breaking in two spacetime dimensions
• Bridging Fermionic and Bosonic Short Range Entangled States
• Spontaneously Broken Subsystem Symmetries
• Fractional Chiral Hinge Insulator
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Fractonic topological phases from coupled wires
• Topological Dipole Conserving Insulators and Multipolar Responses
• Weyl Semimetal from the Honeycomb Array of Topological Insulator Nanowires
• Higher-order topological phase without crystalline symmetry
• Corner Modes and Ground-State Degeneracy in Models with Gauge-Like Subsystem Symmetries

Cited by in corpus (14)

• Unified characterization for higher-order topological phase transitions
• Fractonic Higher-Order Topological Phases in Open Quantum Systems
• Intrinsically Interacting Higher-Order Topological Superconductors
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Classification and construction of interacting fractonic higher-order topological phases
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Fractional chiral second-order topological insulator from a three-dimensional array of coupled wires
• Coupled-wire construction of non-Abelian higher-order topological phases