Related papers: Boundary criticality and multifractality at the 2D…
The critical behavior of quantum Hall transitions in two-dimensional disordered electronic systems can be described by a class of complicated, non-unitary conformal field theories with logarithmic correlations. The nature and the physical…
To probe the universality class of the quantum Hall system at the metal-insulator critical point, the multifractality of the wave function $\psi$ is studied for higher Landau levels, $N=1,2$, for various range $(\sigma )$ of random…
We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical…
Recently, a concept of generalized multifractality, which characterizes fluctuations and correlations of critical eigenstates, was introduced and explored for all ten symmetry classes of disordered systems. Here, by using the non-linear…
We consider the spin quantum Hall transition which may occur in disordered superconductors with unbroken SU(2) spin-rotation symmetry but broken time-reversal symmetry. Using supersymmetry, we map a model for this transition onto the…
We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, based on the theory of conformal restriction. This is a mathematical theory that was recently…
Localization-delocalization transition in a discrete Anderson nonlinear Schr\"odinger equation with disorder is shown to be a critical phenomenon $-$ similar to a percolation transition on a disordered lattice, with the nonlinearity…
The spin quantum Hall (or class C) transition represents one of the few localization-delocalization transitions for which some of the critical exponents are known exactly. Not known, however, is the multifractal spectrum, $\tau_q$, which…
We study the multifractality (MF) of critical wave functions at boundaries and corners at the metal-insulator transition (MIT) for noninteracting electrons in the two-dimensional (2D) spin-orbit (symplectic) universality class. We find that…
The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterised by the surface scaling dimension $\xt$. We consider the case when the boundary…
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…
It is believed that the two-dimensional (2D) Anderson model exhibits localization for any nonzero disorder in the thermodynamic limit and it is also well known that the finite-size effects are considerable in the weak disorder limit. Here…
To understand the finite-size-scaling properties of phases transitions in classical and quantum models in the presence of quenched disorder, it has proven to be fruitful to introduce the notion of a finite-size-pseudo-critical point in each…
We clarify novel forms of scaling functions of conductance, critical conductance distribution and localization length in a disorder-driven quantum phase transition between band insulator and Weyl semimetal phases. Quantum criticality of the…
Multifractals arise in various systems across nature whose scaling behavior is characterized by a continuous spectrum of multifractal exponents $\Delta_q$. In the context of Anderson transitions, the multifractality of critical wave…
Anomalously localized states (ALS) at the critical point of the Anderson transition are studied for the SU(2) model belonging to the two-dimensional symplectic class. Giving a quantitative definition of ALS to clarify statistical properties…
Stationary wave functions at the transition between plateaus of the integer quantum Hall effect are known to exhibit multi-fractal statistics. Here we explore this critical behavior for the case of scattering states of the…
Three-dimensional quantum percolation problems are studied by analyzing energy level statistics of electrons on maximally connected percolating clusters. The quantum percolation threshold $\pq$, which is larger than the classical…
The wavefunctions of a disordered two-dimensional electron gas at the quantum-critical Anderson transition are predicted to exhibit multifractal scaling in their real space amplitude. We experimentally investigate the appearance of these…
We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the…