Related papers: Comment on ``Scaling in Plateau-Plateau Transition…

The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and…

We consider long-range correlated disorder and mutual interacting particles according to a dipole-dipole coupling as modifications to the one-dimensional Anderson model. Technically we rely on the (numerical) exact diagonalization of the…

The 2D system of electron confined to the lowest Landau level is described using a representation of the density matrix depending both on electron and hole coordinates. Condensation of the electron system into a fractional quantum Hall…

There has been a recent revival in understanding the spontaneous scalarization phenomenon in scalar-tensor gravity as a phase transition. Using the tools of the Landau theory, we now know that first-order transitions where scalarization…

We investigate, analytically and numerically, the effects of disorder on the density of states and on the localization properties of the relativistic two dimensional fermions in the lowest Landau level. Employing a supersymmetric technique,…

Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…

An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that…

In a recent Rapid Communication ``Observation of the $\nu=1$ quantum Hall effect in a strongly localized two-dimensional system,'' Shahar, Tsui, and Cunningham reported a disorder --- magnetic field phase diagram for the integer quantum…

Low-energy magnon bands in a two-dimensional spin ice model become integer quantum magnon Hall bands. By calculating the localization length and the two-terminal conductance of magnon transport, we show that the magnon bands with disorders…

This paper revisits the proof of Anderson localization for multi-particle systems. We introduce a multi-particle version of the eigensystem multi-scale analysis by Elgart and Klein, which had previously been used for single-particle…

We give a widely self-contained introduction to the mathematical theory of the Anderson model. After defining the Anderson model and determining its almost sure spectrum, we prove localization properties of the model. Here we discuss…

A Comment on the Letter by Atsushi Ikeda and Kunimasa Miyazaki, [arXiv:1003.5472v2, Phys. Rev. Lett. 104, 255704 (2010)].

This is a chapter for the book "Understanding Quantum Phase Transitions" edited by Lincoln D. Carr (Taylor & Francis, Boca Raton, 2010)

We show that the plateau transitions in the quantum Hall effect is the same as the dimerization transition of a half-filled, one dimensional, $U(2n)$ Hubbard model at $n=0$. We address the properties of the latter by a combination of…

We consider models for the plateau transition in the integer quantum Hall effect. Starting from the network model, we construct a mapping to the Dirac Hamiltonian in two dimensions. In the general case, the Dirac Hamiltonian has randomness…

We use the inverse participation ratio based on the Husimi function to perform a phase space analysis of the Anderson model in one, two, and three dimensions. Important features of the quantum states remain observable in phase space in the…

We review the present status of the Anderson transition in the spectrum of the Dirac operator of QCD-like theories on the lattice. Localized modes at the low-end of the spectrum have been found in SU(2) Yang-Mills theory with overlap and…

We argue that a system of interacting D-branes, generalizing a recent proposal, can be modelled as a Quantum Hall fluid. We show that tachyon condensation in such a system is equivalent to one particle tunnelling. In a conformal field…

Using the level--spacing distribution and the total probability function of the numbers of levels in a given energy interval we analyze the crossover of the level statistics between the delocalized and the localized regimes. By numerically…

The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting…