Virtual Topological Insulators with Real Quantized Physics

Abstract

A concrete strategy is presented for generating strong topological insulators in $d+d^{\prime }$ dimensions which have quantized physics in $d$ dimensions. Here, $d$ counts the physical and $d^{\prime }$ the virtual dimensions. It consists of seeking $d$-dimensional representations of operator algebras which are usually defined in $d+d^{\prime }$ dimensions where topological elements display strong topological invariants. The invariants are shown, however, to be fully determined by the physical dimensions, in the sense that their measurement can be done at fixed virtual coordinates. We solve the bulk-boundary correspondence and show that the boundary invariants are also fully determined by the physical coordinates. We analyze the virtual Chern insulator in $(1+1)$-dimensions realized in Ref.~\cite{KrausPRL2012hh} and predict quantized forces at the edges. We generate a novel topological system in $(3+1)$-dimensions, which is predicted to have quantized magneto-electric response.

Proof that the invariants can be computed at fixed virtual coordinate is included

References in corpus (23)

• Topological States and Adiabatic Pumping in Quasicrystals
• The Non-Commutative Geometry of the Quantum Hall Effect
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Edge states and topological phases in one-dimensional optical superlattices
• Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Orbital magnetoelectric coupling in band insulators
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Disordered Topological Insulators: A Non-Commutative Geometry Perspective
• Measurement of a topological edge invariant in a microwave network
• Simultaneous quantization of edge and bulk Hall conductivity
• Anomalous transport: a mathematical framework
• Topological equivalence of crystal and quasicrystal band structures
• The non-commutative n-th Chern number
• Quantum transport in disordered systems under magnetic fields: A study based on operator algebras
• The Ten Martini Problem
• Orbital polarization and magnetization for independent particles in disordered media
• A Non-Commutative Formula for the Isotropic Magneto-Electric Response
• Topological quantization of boundary forces and the integrated density of states
• Rotation Numbers, Boundary Forces and Gap labelling

Cited by in corpus (40)

• Non-Hermitian Physics
• Topological phase transition in non-Hermitian quasicrystals
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Experimental observation of temporal pumping in electro-mechanical waveguides
• Observation of topological edge modes in a quasi-periodic acoustic waveguide
• Complex classes of periodically driven topological lattice systems
• Experimental Demonstration of Dynamic Topological Pumping Across Incommensurate Bilayered Acoustic Metamaterials
• The 6D quantum Hall effect and 3D topological pumps
• Topological states in quasicrystals
• Characterization of topological phase transitions via topological properties of transition points
• Topological Edge Modes by Smart Patterning
• Non-Commutative Chern Numbers for Generic Aperiodic Discrete Systems
• High-order topological insulators from high-dimensional Chern insulators
• Exploring Topology of 1D Quasiperiodic Metastructures through Modulated LEGO Resonators
• Differential topology of semimetals
• Topological Gaps by Twisting
• Quantum many-body topology of quasicrystals
• T-duality simplifies bulk-boundary correspondence
• The K-Theoretic Bulk-Boundary Principle for Dynamically Patterned Resonators
• Material vs. structure: Topological origins of band-gap truncation resonances in periodic structures
• Rational Approximations of Quasi-Periodic Problems via Projected Green's Functions
• Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis
• Mechanics and dynamics of two-dimensional quasiperiodic composites
• Localization via Quasi-Periodic Bulk-Bulk Correspondence
• T-duality simplifies bulk-boundary correspondence: some higher dimensional cases
• Bulk-boundary correspondance for Sturmian Kohmoto like models
• Linking topological features of the Hofstadter model to optical diffraction figures
• Fractal defect states in the Hofstadter butterfly
• Fractional Topological States in Quantum Spin Chains with Periodical Modulation
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• Coexistence of 1D and 2D topology and genesis of Dirac cones in the chiral Aubry-André model
• Topology in quasicrystals
• Quasiperiodicity protects quantized transport in disordered systems without gaps
• C*-framework for higher-order bulk-boundary correspondences
• Topological charge and spin pumping in a semiconductor nanowire
• Physical rendering of synthetic spaces for topological sound transport
• Quasiperiodic Quadrupole Insulators
• Reentrant topology and reverse pumping in a quasiperiodic flux ladder
• Mapping Chern numbers in quasi-periodic interacting spin chains