Related papers: Wave function statistics and multifractality at th…
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…
We study numerically multifractal properties of two models of one-dimensional quantum maps, a map with pseudointegrable dynamics and intermediate spectral statistics, and a map with an Anderson-like transition recently implemented with cold…
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…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
Repeated local measurements of quantum many body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases…
Macroscopic systems often display phase transitions where certain physical quantities are singular or self-similar at different (spatial) scales. Such properties of systems are currently characterized by some order parameters and a few…
We study the statistical correlation functions for the three-dimensional hydrodynamic turbulence onset when the dynamics is dominated by the pancake-like high-vorticity structures. With extensive numerical simulations, we systematically…
Critical fluctuations of wave functions and energy levels at the Anderson transition are studied for the family of the critical power-law random banded matrix ensembles. It is shown that the distribution functions of the inverse…
We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results…
Multifractal properties of wave functions in a disordered system can be derived from self-consistent theory of localization by Vollhardt and Woelfle. A diagrammatic interpretation of results allows to obtain all scaling relations used in…
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…
In this work we put forward an effective Gaussian free field description of critical wavefunctions at the transition between plateaus of the integer quantum Hall effect. To this end, we expound our earlier proposal that powers of critical…
We study the spectral and wavefunction properties of a one-dimensional incommensurate system with p-wave pairing and unveil that the system demonstrates a series of particular properties in its ciritical region. By studying the spectral…
We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wavefunctions at the transition energy are obtained within the…
We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions subject to projective monitoring of local charge across the measurement-induced phase transition. Our observables are…
We present a theoretical framework for understanding the wavefunctions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong…
We develop the concept of surface multifractality for localization-delocalization (LD) transitions in disordered electronic systems. We point out that the critical behavior of various observables related to wave functions near a boundary at…
We study a system of two tunnel-coupled quantum dots, with the first dot containing interacting electrons (described by the Universal Hamiltonian) not subject to spin-orbit coupling, whereas the second contains non-interacting electrons…
We propose a resolution of the renormalization group flow for the disordered Dirac fermion theories describing the quantum Hall transition (QHT) and spin Quantum Hall transition (SQHT), which previously revealed no perturbative fixed points…
The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at…