Related papers: Topology vs. Anderson localization: non-perturbati…
We study the disorder effect on the transport properties in the HgTe/CdTe semiconductor quantum wells. We confirm that at a moderate disorder strength, the initially un-quantized two terminal conductance becomes quantized, and the system…
We establish an important duality correspondence between topological order in quantum many body systems and criticality in ferromagnetic classical spin systems. We show how such a correspondence leads to a classical and simple procedure for…
We propose a new viewpoint on the study of localization transitions in disordered quantum systems, showing how critical properties can be seen also as a geometric transition in the data space generated by the classically encoded…
Using a three-frequency one-dimensional kicked rotor experimentally realized with a cold atomic gas, we study the transport properties at the critical point of the metal-insulator Anderson transition. We accurately measure the…
The parametric motion of energy levels for non-interacting electrons at the Anderson localization critical point is studied by computing the energy level-curvatures for a quasiperiodic ring with twisted boundary conditions. We find a…
Topological insulators are newly discovered materials with the defining property that any boundary cut into such crystal supports spectrum which is immune to the Anderson localization. The present paper summarizes our efforts on the…
We study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined for infinite (bulk) or half-infinite (edge) systems, and it…
The quantum anomalous Hall system with Chern number 2 can be destroyed by sufficiently strong disorder. During its process towards localization, it was found that the electronic states will be directly localized to an Anderson insulator…
The combination of topology and quantum criticality can give rise to an exotic mix of counterintuitive effects. Here, we show that unexpected topological properties take place in a paradigmatic strongly-correlated Hamiltonian: the 1D…
We study the ground state of the two-dimensional Anderson-Hubbard model using a quantum real space renormalization group method. We obtain the phase diagram near half filling. The system is always insulating with disorder. At half filling,…
Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the…
We study topological insulators under dephasing noise. With examples of both a $2d$ Chern insulator and a $3d$ topological insulator protected by time-reversal symmetry, we demonstrate that there is a phase transition at finite dephasing…
We propose general topological order parameters for interacting insulators in terms of the Green's function at zero frequency. They provide an unified description of various interacting topological insulators including the quantum anomalous…
We study Anderson localization in disordered tight-binding models on hyperbolic lattices. Such lattices are geometries intermediate between ordinary two-dimensional crystalline lattices, which localize at infinitesimal disorder, and Bethe…
The quantum Coulomb glass model describes disordered interacting electrons on the insulating side of a metal-insulator transition. By taking quantum fluctuations into account it can describe not only the localized limit but also the weakly…
In this paper, we discuss the characteristic features of one-dimensional topological insulators with inversion symmetry but noncentered inversion axis in the unit cell, for any choice of the unit cell. In these systems, the global inversion…
We present models of topological insulating Hamiltonians exhibiting intrinsic altermagnetic features, protected by combined three-fold or four-fold rotational symmetries with time-reversal. We demonstrate that the spin Chern number serves…
It has been proposed recently by some of the authors that the quantum phase transition of a topological insulator like the SSH model may be detected by the eigenvalues and eigenvectors of the reduced density matrix. Here we further extend…
Topology in quantum systems is typically considered in infinite crystals in one, two, or higher integer dimensions. Here, we show that one can continuously transform a system between a topological phase associated with one dimension and a…
We propose to use generic Chern numbers for a characterization of topological insulators. It is suitable for a numerical characterization of low dimensional quantum liquids where strong quantum fluctuations prevent from developing…