Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder

Abstract

The chiral AIII symmetry class in the periodic table of topological insulators contains topological phases classified by a winding number $\nu$ for each odd space-dimension. An open problem for this class is the characterization of the phases and phase-boundaries in the presence of strong disorder. In this work, we derive a covariant real-space formula for $\nu$ and, using an explicit 1-dimensional disordered topological model, we show that $\nu$ remains quantized and non-fluctuating when disorder is turned on, even though the bulk energy-spectrum is completely localized. Furthermore, $\nu$ remains robust even after the insulating gap is filled with localized states, but when the disorder is increased even further, an abrupt change of $\nu$ to a trivial value is observed. Using exact analytic calculations, we show that this marks a critical point where the localization length diverges. As such, in the presence of disorder, the AIII class displays a markedly different physics from everything known to date, with robust invariants being carried entirely by localized states and bulk extended states emerging from an absolutely localized spectrum. Detailed maps and a clear physical description of the phases and phase boundaries are presented based on numerical and exact analytic calculations.

5 pages 2 figures + 5 pages, 1 figure supplementary information

References in corpus (32)

• Maximally-localized generalized Wannier functions for composite energy bands
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Entanglement Entropy and Quantum Field Theory
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• The Non-Commutative Geometry of the Quantum Hall Effect
• Inversion Symmetric Topological Insulators
• Exponential localization of Wannier functions in insulators
• Entanglement entropy of random quantum critical points in one dimension
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Scattering formula for the topological quantum number of a disordered multi-mode wire
• Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples
• The insulator/Chern-insulator transition in the Haldane model
• Disordered Topological Insulators: A Non-Commutative Geometry Perspective
• Chiral Topological Insulators, Superconductors and other competing orders in three dimensions
• Localization in a quantum spin Hall system
• Delocalization Transition via Supersymmetry in one Dimension
• Topological Insulators and C^*-Algebras: Theory and Numerical Practice
• Random Bonds and Topological Stability in Gapped Quantum Spin Chains
• Quantum criticality of quasi one-dimensional topological Anderson insulators
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Criticality and entanglement in random quantum systems
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
• Almost Commuting Matrices, Localized Wannier Functions, and the Quantum Hall Effect
• The non-commutative n-th Chern number
• Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant
• Quantum transport in disordered systems under magnetic fields: A study based on operator algebras
• Topologically Protected Extended States in Disordered Quantum Spin-Hall Systems without Time-Reversal Symmetry
• Signature of Phase Transitions in the Disordered Quantum Spin Hall State From the Entanglement Spectrum

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