Topological Dipole Conserving Insulators and Multipolar Responses

Abstract

Higher order topological insulators (HOTIs) are a novel form of insulating quantum matter, which are characterized by having gapped boundaries that are separated by gapless corner or hinge states. Recently, it has been proposed that the essential features of a large class of HOTIs are captured by topological multipolar response theories. In this work, we show that these multipolar responses can be realized in interacting lattice models, which conserve both charge and dipole. In this work we study several models in both the strongly interacting and mean-field limits. In $2$D we consider a ring-exchange model which exhibits a quadrupole response, and can be tuned to a $C_4$ symmetric higher order topological phase with half-integer quadrupole moment, as well as half-integer corner charges. We then extend this model to develop an analytic description of adiabatic dipole pumping in an interacting lattice model. The quadrupole moment changes during this pumping process, and if the process is periodic, we show the total change in the quadrupole moment is quantized as an integer. We also consider two interacting $3$D lattice models with chiral hinge modes. We show that the chiral hinge modes are heralds of a recently proposed "dipolar Chern-Simons" response, which is related to the quadrupole response by dimensional reduction. Interestingly, we find that in the mean field limit, both the $2$D and $3$D interacting models we consider here are equivalent to known models of non-interacting HOTIs (or boundary obstructed versions). The self-consistent mean-field theory treatment provides insight into the connection between free-fermion (mean-field) theories having vanishing polarization and interacting models where dipole moments are microscopically conserved.

arXiv comment28 pages, 16 figures

References in corpus (52)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological invariants of time-reversal-invariant band structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Periodic table for topological insulators and superconductors
• Topological quantum chemistry
• Topological Crystalline Insulators in the SnTe Material Class
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Symmetry protected topological orders and the group cohomology of their symmetry group
• $(d-2)$-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
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Local stabilizer codes in three dimensions without string logical operators
• Three-Dimensional Topological Insulators
• Symmetry Protected Topological phases of Quantum Matter
• Inversion Symmetric Topological Insulators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Fractons
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Fracton Phases of Matter
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• Fracton-Elasticity Duality
• The Fracton Gauge Principle
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Topological phases protected by point group symmetry
• Gauging spatial symmetries and the classification of topological crystalline phases
• Field Theories With a Vector Global Symmetry
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Emergent Gravity of Fractons: Mach's Principle Revisited
• Chiral Topological Elasticity and Fracton Order
• Boundary-obstructed topological phases
• Theory of interacting topological crystalline insulators
• Axion topological field theory of topological superconductors
• Emergent Gravity at a Lifshitz Point from a Bose Liquid on the Lattice
• Fractons from Partons
• Multipolar Topological Field Theories: Bridging Higher Order Topological Insulators and Fractons
• Anomaly Cancellation in 2+1 dimensions in the presence of a domainwall mass
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Higher-form Gauge Symmetries in Multipole Topological Phases
• Theory of Dipole Insulators
• Intrinsically interacting topological crystalline insulators and superconductors
• Entanglement Signatures of Multipolar Higher Order Topological Phases

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• Fractonic Higher-Order Topological Phases in Open Quantum Systems
• Hierarchical hydrodynamics in long-range multipole-conserving systems
• Classification and construction of interacting fractonic higher-order topological phases
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• Topological Dipole Insulator