Related papers: On the critical level-curvature distribution
Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our…
We study a non-Hermitian Aubry-Andr\'e-Harper model with both nonreciprocal hoppings and complex quasiperiodical potentials, which is a typical non-Hermitian quasicrystal. We introduce boundary-dependent self-dualities in this model and…
We consider the properties of the random regular graph with node degree $d$ perturbed by chemical potentials $\mu_k$ for a number of short $k$-cycles. We analyze both numerically and analytically the phase diagram of the model in the…
The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams…
We study numerically and analytically the moments of the dimensionless level curvature for one-dimensional disordered rings of the circumference L pierced by a magnetic flux. The negative moments of the curvature distribution can be…
The quantum Coulomb glass model describes disordered interacting electrons on the insulating side of a metal-insulator transition. By taking quantum fluctuations into account it can describe not only the localized limit but also the weakly…
The universal critical point ratio $Q$ is exploited to determine positions of the critical Ising transition lines on the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the ratio $Q$ in the…
In this study, we investigate the problem of Anderson localization in a one-dimensional flat band lattice with a non-Hermitian quasiperiodic on-site potential. First of all, we discuss the influences of non-Hermitian potentials on the…
We present a full description of the nonergodic properties of wavefunctions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two critical localization…
Why life persists at the edge of chaos is a question at the very heart of evolution. Here we show that molecules taking part in biochemical processes from small molecules to proteins are critical quantum mechanically. Electronic…
We study electron localization in disordered quantum systems, focusing on both individual eigenstates and thermal states. We employ complex polarization as a numerical indicator to characterize the system's localization length. Furthermore,…
We study non-interacting systems with a power-law quasiparticle dispersion $\xi_{\bf k}\propto k^\alpha$ and a random short-range-correlated potential. We show that, unlike the case of lower dimensions, for $d>2\alpha$ there exists a…
We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum…
A model in which a three-dimensional elastic medium is represented by a network of identical masses connected by springs of random strengths and allowed to vibrate only along a selected axis of the reference frame, exhibits an Anderson…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
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…
Based on quantum theory, we investigate the distribution of the electrons scattered in nonlinear Compton effect by an electromagnetic plane wave. Deviations of the final electron momentum from its initial value are solely due to quantum…
Chiral Random Matrix Theory has proven to describe the spectral properties of low temperature QCD very well. However, at temperatures above the chiral symmetry restoring transition it can not provide a global description. The level-spacing…
A new perturbational approach to spectral and thermal properties of strongly correlated electron systems is presented: The Anderson model is reexamined for $U\to\infty$\,, and it is shown that an expansion of Green's functions with respect…
Paper reviews recent numerical data for the conductance distribution of disordered systems in the critical regime and in the localized regime. Of particular interest is the non-analytical form of the critical conductance distribution in the…