AIII and BDI Topological Systems at Strong Disorder

Abstract

Using an explicit 1-dimensional model, we provide direct evidence that the one-dimensional topological phases from the AIII and BDI symmetry classes follow a $\mathbb{Z}$-classification, even in the strong disorder regime when the Fermi level is embedded in a dense localized spectrum. The main tool for our analysis is the winding number $\nu$, in the non-commutative formulation introduced in I. Mondragon-Shem, J. Song, T. L. Hughes, and E. Prodan, arXiv:1311.5233. For both classes, by varying the parameters of the model and/or the disorder strength, a cascade of sharp topological transitions $\nu =0\to \nu =1\to \nu =2$ is generated, in the regime where the insulating gap is completely filled with the localized spectrum. We demonstrate that each topological transition is accompanied by an Anderson localization-delocalization transition. Furthermore, to explicitly rule out a ${\mathbb{Z}}_2$ classification, a topological transition between $\nu =0$ and $\nu =2$ is generated. These two phases are also found to be separated by an Anderson localization-delocalization transition, hence proving their distinct identity.

10 pages and 8 figures; one figure was added and some paragraphs were updated

References in corpus (8)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Anderson Insulator
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Topological Anderson Insulator in Three Dimensions
• The dependence of topological Anderson insulator on the type of disorder
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
• Manifestly gauge independent formulations of the Z2 invariants

Cited by in corpus (68)

• Observation of the topological Anderson insulator in disordered atomic wires
• Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Disorder and metal-insulator transitions in Weyl semimetals
• Skin effect and winding number in disordered non-Hermitian systems
• An atom optics approach to studying lattice transport phenomena
• Topological Weaire-Thorpe models of amorphous matter
• Topological Anderson Insulator in electric circuits
• Many-body topological invariants in fermionic symmetry protected topological phases: Cases of point group symmetries
• Real-space representation of winding number for one-dimensional chiral-symmetric topological insulator
• Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices
• Dual topological characterization of non-Hermitian Floquet phases
• Non-Hermitian Floquet Topological Matter -- A Review
• Real space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems
• Anderson localization and the topology of classifying spaces
• Computation of topological phase diagram of disordered Pb${}_{1-x}$Sn${}_x$Te using the kernel polynomial method
• Winding numbers of phase transition points for one-dimensional topological systems
• Disorder-induced topological phase transition in a 1D mechanical system
• Bulk-boundary correspondence in point-gap topological phases
• Disorder Effects in Topological States -- Brief Review of the Recent Developments
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice
• Persistence of chirality in the Su-Schrieffer-Heeger model in the presence of on-site disorder
• Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
• Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Disordered Chern insulator with a two step Floquet drive
• Effect of Strong Disorder on 3-Dimensional Chiral Topological Insulators: Phase Diagrams, Maps of the Bulk Invariant and Existence of Topological Extended Bulk States
• Disorder driven phase transitions in weak AIII topological insulators
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
• Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker
• Phase diagrams of Weyl semimetals with competing intraorbital and interorbital disorders
• Real spectra, Anderson localization, and topological phases in one-dimensional quasireciprocal systems
• Generalization of spectral bulk-boundary correspondence
• Dimensional evolution between one- and two-dimensional topological phases
• Topological states in disordered arrays of dielectric nanoparticles
• Floquet second-order topological Anderson insulator hosting corner localized modes
• Critical Behaviors of Anderson Transitions in Three Dimensional Orthogonal Classes with Particle-hole Symmetries
• Anatomy of topological Anderson transitions
• Floquet topological transitions in extended Kane-Mele models with disorder
• Weak quantization of non-interacting topological Anderson insulator
• Topological Modes in One Dimensional Solids and Photonic Crystals
• Topological Corner States in Graphene by Bulk and Edge Engineering
• Quantization of topological indices in critical chains at low temperatures
• Robust measurement of wave function topology on NISQ quantum computers
• On the relation of the entanglement spectrum to the bulk polarization
• Topological phase transition in disordered elastic quantum spin Hall system
• Topologically localized insulators
• Probing the Topological Anderson Transition in Quasiperiodic Photonic Lattices via Chiral Displacement and Wavelength Tuning
• Topological states constructed by two different trivial quantum wires
• Flow of unitary matrices: Real-space winding numbers in one and three dimensions
• Topological Anderson insulator phases in one dimensional quasi-periodic mechanical SSH chains
• Kitaev Chain with a Fractional Twist
• The $\pi$ Berry Phase and Topological Excitation in Interacting Boson-Fermion Mixtures
• Topological Anderson insulators by latent symmetry
• Many topological regions on the Bloch sphere of the spin-1/2 double kicked top
• Quantum oscillation in Hopf-link semimetals
• Regularized universal topological markers for Dirac systems
• Recent progress on disorder-induced topological phases
• Two-particle topological Thouless spin pump
• Multiple reentrant topological windows induced by generalized Bernoulli disorder
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• Disorder driven topological phase transitions in 1D mechanical quasicrystals
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Characterizing the transition from topology to chaos in a kicked quantum system
• Universal localization-delocalization transition in chiral-symmetric Floquet drives
• Anomalous Non-Hermitian Topological Anderson Insulator