Theory of Dipole Insulators

Abstract

Insulating systems are characterized by their insensitivity to twisted boundary conditions as quantified by the charge stiffness and charge localization length. The latter quantity was shown to be related to the expectation value of the many-body position operator and serves as a universal criterion to distinguish between metals and insulators. In this work we extend these concepts to a new class of quantum systems having conserved charge and dipole moments. We refine the concept of a charge insulator by introducing notions of multipolar insulators, e.g., a charge insulator could be a dipole insulator or dipole metal. We develop a universal criterion to distinguish between these phases by extending the concept of charge stiffness and localization to analogous versions for multipole moments, but with our focus on dipoles. We are able relate the dipole localization scale to the expectation value of a recently introduced many-body quadrupole operator. This refined structure allows for the identification of phase transitions where charge remains localized but, e.g., dipoles delocalize. We illustrate the proposed criterion using several exactly solvable models that exemplify these concepts, and discuss a possible realization in cold-atom systems.

arXiv comment11+4 pages, 2 figures

References in corpus (55)

• Maximally-localized generalized Wannier functions for composite energy bands
• Unpaired Majorana fermions in quantum wires
• Quantized Electric Multipole Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• Bose-Einstein Condensation of Excitons in Bilayer Electron Systems
• Local stabilizer codes in three dimensions without string logical operators
• The Quantum-Mechanical Position Operator in Extended Systems
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Electron Localization in the Insulating State
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Polarization and localization in insulators: generating function approach
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• Fracton-Elasticity Duality
• Integrability and ideal conductance at finite temperatures
• The Fracton Gauge Principle
• Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
• Ring exchange, the Bose metal, and bosonization in two dimensions
• Subsystem symmetry protected topological order
• Fracton Models on General Three-Dimensional Manifolds
• Fracton topological order via coupled layers
• Fractal symmetries: Ungauging the cubic code
• Towards classification of Fracton phases: the multipole algebra
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Many-Body Electric Multipole Operators in Extended Systems
• Chiral Topological Elasticity and Fracton Order
• Many-Body Order Parameters for Multipoles in Solids
• Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Dualities
• Fracton topological phases from strongly coupled spin chains
• Topological Entanglement Entropy of Fracton Stabilizer Codes
• D-wave correlated Critical Bose Liquids in two dimensions
• Fractional excitations in foliated fracton phases
• Fractal Symmetric Phases of Matter
• Quantum-Mechanical Position Operator and Localization in Extended Systems
• X-Cube Fracton Model on Generic Lattices: Phases and Geometric Order
• Classification of subsystem symmetry-protected topological phases
• Symmetric Fracton Matter: Twisted and Enriched
• Fractons from Partons
• Pinch Point Singularities of Tensor Spin Liquids
• Symmetric Tensor Gauge Theories on Curved Spaces
• Finite-temperature Drude weight within the anisotropic Heisenberg chain
• Fractonic line excitations : an inroad from 3d elasticity theory
• Scalar Field Theories with Polynomial Shift Symmetries
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Higher Rank Deconfined Quantum Criticality at the Lifshitz Transition and the Exciton Bose Condensate
• Electron Localization in the Quantum-Hall Regime
• Higher Order Bosonic Topological Phases in Spin Models
• Finite-Temperature Screening of U(1) Fractons
• Study of a hard-core boson model with ring-only interactions
• Possible realization of the Exciton Bose Liquid phase in a hard-core boson model with ring-only exchange interactions
• Theory for electric dipole superconductivity with an application for bilayer excitons

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• Lieb Schultz Mattis-Type Theorems and Other Non-perturbative Results for Strongly Correlated Systems with Conserved Dipole Moments
• Topological Dipole Conserving Insulators and Multipolar Responses
• Filling constraints on translation invariant dipole conserving systems
• Phase diagram and topology of the XXZ chain with alternating bonds and staggered magnetic field
• Topological Dipole Insulator
• Electromagnetic response in dipole superfluids: vortex lattices and singular domain walls
• Domain coarsening in fractonic systems: a cascade of critical exponents