Related papers: Multifractality at the quantum Hall transition: Be…
We study numerically conductance fluctuations near the integer quantum Hall effect plateau transition. The system is presumed to be in a mesoscopic regime, with phase coherence length comparable to the system size. We focus on a…
The quantum Hall effect in ultra-high mobility GaAs/AlGaAs has been measured and plateaus are found at many different fractions. The resistivity is quantized as \rho =h/ie^2 where i exhibits many different values. The fractions 5/3, 8/5,…
We explore the critical properties of a topological transition in a two-dimensional, amorphous lattice with randomly distributed points. The model intrinsically breaks the time-reversal symmetry without an external magnetic field, akin to a…
We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the $\nu=2$ and the $\nu=1$ quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall…
While quantum multifractality has been widely studied in the physics literature and is by now well understood from the point of view of physics, there is little work on this subject in the mathematical literature. I will report on a proof…
We analyze the scaling behavior at and near a quantum critical point separating a semimetallic from a superfluid phase. To this end we compute the renormalization group flow for a model of attractively interacting electrons with a linear…
We systematically study the acousto-current of two-dimensional electron systems in the integer and fractional quantum Hall regimes using surface acoustic waves. We are able to separate the co-existing acoustic scattering and drag, when…
We use multifractal finite-size scaling to perform a high-precision numerical study of the critical properties of the Anderson localization-delocalization transition in the unitary symmetry class, considering the Anderson model including a…
The double layer $\nu=2/3$ fractional quantum Hall system is studied using the edge state formalism and finite-size diagonalization subject to periodic boundary conditions. Transitions between three different ground states are observed as…
We calculate perturbatively the multifractality spectrum of wave-functions in critical random matrix ensembles in the regime of weak multifractality. We show that in the leading order the spectrum is universal, while the higher order…
We address two fundamental issues in the physics of the quantum Hall effect: a unified description of scaling behavior of conductances in the integral and fractional regimes, and a quasi-particle formulation of the chiral Luttinger Liquids…
The transition from the quantum Hall state to the insulator is considered for non-interacting electrons in a two-dimensional disordered lattice model with perpendicular magnetic field. Using correlated random disorder potentials the…
Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…
We consider the one dimensional classical Ising model in a symmetric dichotomous random field. The problem is reduced to a random iterated function system for an effective field. The D_q-spectrum of the invariant measure of this effective…
Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving…
We review the quantum spectral curve (QSC) formalism for anomalous dimensions of planar ${\cal\ N}=4$ SYM, including its $\gamma$-deformation. Leaving aside its derivation, we concentrate on formulation of the "final product" in its most…
This paper studies the spectrum of a multi-dimensional split-step quantum walk with a defect that cannot be analysed in the previous papers. To this end, we have developed a new technique which allow us to use a spectral mapping theorem for…
The statistics of energy levels of electrons in a random potential is considered in the critical energy window near the mobility edge. It is shown that the multifractality of critical wave functions results in the violation of the…
Quadratic band crossing points (QBCPs) and quantum anomalous Hall effect (QAHE) have attracted the attention of both theoretical and experimental researchers in recent years. Based on first-principle calculations, we find that the FeB$_2$…
We study the metal-insulator transition on a three dimensional quantum percolation model by analyzing energy level statistics. The quantum percolation threshold $\pq$, which is larger than the classical percolation threshold $\pc$, becomes…