# Anderson localization and the topology of classifying spaces

@article{Morimoto2015AndersonLA, title={Anderson localization and the topology of classifying spaces}, author={Takahiro Morimoto and Akira Furusaki and Christopher Mudry}, journal={Physical Review B}, year={2015}, volume={91}, pages={235111} }

In this work the authors generate the ten-fold classification of the periodic table of topological insulators by studying random Dirac Hamiltonians supporting a Dirac mass. They use homotopy groups to establish the phase diagram that encodes Anderson localization and provide an alternative explanation for the even-odd effect in the one-dimensional chiral classes.

## Figures and Tables from this paper

## 25 Citations

Fractional Abelian topological phases of matter for fermions in two-dimensional space

- Physics
- 2017

These notes constitute chapter 7 from "l'Ecole de Physique des Houches" Session CIII, August 2014 dedicated to Topological Aspects of Condensed matter physics. The tenfold way in…

Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics

- Physics, Mathematics
- 2016

Illustration of key concepts in dimension d = 1.- Topological solid state systems: conjectures, experiments and models.- Observables algebras for solid state systems.- K-theory for topological solid…

Localized surfaces of three-dimensional topological insulators

- PhysicsPhysical Review B
- 2019

We study the surface of a three-dimensional spin chiral $\mathrm{Z}_2$ topological insulator (class CII), demonstrating the possibility of its localization. This arises through an interplay of…

Classification of topological quantum matter with symmetries

- Physics
- 2016

Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum…

Metal or insulator? Dirac operator spectrum in holographic QCD

- PhysicsPhysics Letters B
- 2019

Abstract The lattice studies in QCD demonstrate the nontrivial localization behavior of the eigenmodes of the 4D Euclidean Dirac operator considered as Hamiltonian of 4 + 1 dimensional disordered…

Topological phase diagram of the disordered 2XY model in presence of generalized Dzyaloshinskii-Moriya Interaction.

- Physics, MedicineJournal of physics. Condensed matter : an Institute of Physics journal
- 2019

The localization length outperforms the standard topological indices in two respects: it is much faster and more accurate to calculate and it can count the winding number of the parent Hamiltonian by looking into the edges of the daughter Hamiltonian.

Anomalous Floquet topological crystalline insulators

- PhysicsPhysical Review B
- 2019

Periodically driven systems can host so-called anomalous topological phases in which protected boundary states coexist with topologically trivial Floquet bulk bands. We introduce an anomalous version…

Mobility edge and Black Hole Horizon

- Physics
- 2018

We conjecture that the mobility edge in the 4D Euclidean Dirac operator spectrum in QCD in the deconfined phase found in the lattice studies corresponds to the near black hole (BH) horizon region in…

Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model

- Physics, Mathematics
- 2015

We establish the connection between a multichannel disordered model --the 1D Dirac equation with $N\times N$ matricial random mass-- and a random matrix model corresponding to a deformation of the…

Quantum Lattice Boltzmann Study of Random-Mass Dirac Fermions in One Dimension

- Physics
- 2018

We study the time evolution of quenched random-mass Dirac fermions in one dimension by quantum lattice Boltzmann simulations. For nonzero noise strength, the diffusion of an initial wave packet stops…