Related papers: Critical parameters from generalised multifractal …
We uncover field-theoretic underpinnings of symmetry relations for multifractal spectra at Anderson transitions and at critical points of other disordered systems. We show that such relations follow from the conformal invariance of the…
For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…
We show that quantum wavepackets exhibit a sharp macroscopic peak as they spread in the vicinity of the critical point of the Anderson transition. The peak gives a direct access to the mutifractal properties of the wavefunctions and…
By using dimensionless conductances as scaling variables, the conventional one-parameter scaling theory of localization fails for non-reciprocal non-Hermitian systems such as the Hanato-Nelson model. Here, we propose a one-parameter scaling…
The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is…
The disorder induced metal--insulator transition is investigated in a three-dimensional simple cubic lattice and compared for the presence and absence of time-reversal and spin-rotational symmetry, i.e. in the three conventional symmetry…
We perform a thorough and complete analysis of the Anderson localization transition on several models of random graphs with regular and random connectivity. The unprecedented precision and abundance of our exact diagonalization data (both…
The three-dimensional Anderson model represents a paradigmatic model to understand the Anderson localization transition. In this work we first review some key results obtained for this model in the past 50 years, and then study its…
The critical dynamics of conformal field theories on random surfaces is investigated beyond the previously studied dynamics of the overall area and the genus. It is found that the evolution of the order parameter in physical time performs a…
Many models and real complex systems possess critical thresholds at which the systems shift from one sate to another. The discovery of the early warnings of the systems in the vicinity of critical point are of great importance to estimate…
Bifractal is a highly anisotropic structure where planar fractals are stacked to form a 3-dimensional lattice. The localization lengths along fractal structure for the Anderson model defined on a bifractal are calculated. The critical…
We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed…
Two exact relations between mutlifractal exponents are shown to hold at the critical point of the Anderson localization transition. The first relation implies a symmetry of the multifractal spectrum linking the multifractal exponents with…
We study the three-dimensional two-band Anderson model of localization and compare our results to experimental results for amorphous metallic alloys (AMA). Using the transfer-matrix method, we identify and characterize the metal-insulator…
We examine statistical fluctuation of eigenvalues from the near-edge bulk of QCD Dirac spectra above the critical temperature. For completeness we start by reviewing on the spectral property of Anderson tight-binding Hamiltonians as…
An order parameter description of the Anderson-Mott transition (AMT) is given. We first derive an order parameter field theory for the AMT, and then present a mean-field solution. It is shown that the mean-field critical exponents are exact…
The single parameter scaling hypothesis is the foundation of our understanding of the Anderson transition. However, the conductance of a disordered system is a fluctuating quantity which does not obey a one parameter scaling law. It is…
Disorder is ubiquitous in solid-state systems, and its crucial influence on transport properties was revealed by the discovery of Anderson localization. Generally speaking, all bulk states will be exponentially localized in the strong…
Diffusive transport is among the most common phenomena in nature [1]. However, as predicted by Anderson [2], diffusion may break down due to interference. This transition from diffusive transport to localization of waves should occur for…
The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. We focus on the character of criticality as well as on underlying symmetries and topologies that are crucial for understanding…