Related papers: Logarithmic Correlations in Quantum Hall Plateau T…
Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing…
We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting…
Multifractal scaling of critical wave functions at a disorder-driven (Anderson) localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin quantum Hall plateau transition using…
As a unified theory of integer and fractional quantum Hall plateau transitions, a nonperturbative theory of the two-parameter scaling renormalization group function is presented. By imposing global symmetries known as ``the law of…
We numerically investigate the effects of disorder on the quantum Hall effect (QHE) and the quantum phase transitions in silicene based on a lattice model. It is shown that for a clean sample, silicene exhibits an unconventional QHE near…
Double layer quantum Hall systems have interesting properties associated with interlayer correlations. At $\nu =1/m$ where $m$ is an odd integer they exhibit spontaneous symmetry breaking equivalent to that of spin $1/2$ easy-plane…
We investigate the role of quantum fluctuations in topological quantum phase transitions of quantum spin Hall insulators and quantum anomalous Hall insulators. Employing the variational cluster approximation to obtain the single-particle…
The quantum Hall effect is one of the most extensively studied topological effects in solid state physics. The transitions between different quantum Hall states exhibit critical phenomena described by universal critical exponents. Numerous…
The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law…
The quantum critical behavior of disordered itinerant ferromagnets is determined exactly by solving a recently developed effective field theory. It is shown that there are logarithmic corrections to a previous calculation of the critical…
We investigate numerically whether the chiral symmetry is the sole factor dominating the criticality of the quantum Hall transitions in disordered graphene. When the disorder respects the chiral symmetry, the plateau-to-plateau transition…
The ground state of a quantum spin chain is a natural playground for investigating correlations. Nevertheless, not all correlations are genuinely of quantum nature. Here we review the recent progress to quantify the 'quantumness' of the…
We study the critical properties of the quantum anomalous Hall (QAH) plateau transition in magnetic topological insulators. We introduce a microscopic model for the plateau transition in QAH effect at the coercive field and then map it to…
Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of critical points in several classes of disordered systems…
We study the quantum correlations in a 2D system that possesses a topological quantum phase transition. The quantumness of two-body correlations is measured by quantum discord. We calculate both the correlation of two local spins and that…
We investigate the interplay of disorder and interaction in two-dimensional electron systems in a strong magnetic field, focusing on the transition between Wigner crystals and fractional quantum Hall liquids. We first study classical Wigner…
We investigate how the criticality of the quantum Hall plateau transition in disordered graphene differs from those in the ordinary quantum Hall systems, based on the honeycomb lattice with ripples modeled as random hoppings. The…
A careful study of the supersymmetric version of Pruisken's nonlinear sigma model for the integer quantum Hall effect is presented. The lattice regularized model is cast in Hamiltonian form by taking the anisotropic limit and interpreting…
The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong perpendicular magnetic field and was later generalized to Chern insulators without net magnetization. Here,…
I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic…