Related papers: Criticality without self-similarity: a 2D system w…
The two-dimensional hyperbolic plane, $\mathbb{H}^2$, is an unusual system in that dimensionality changes with scale: locally two-dimensional and planar at short distances, but effectively infinite-dimensional at large scales, it provides…
The critical behaviour of 3-dimensional disordered systems in a strong magnetic field is investigated by analysing the spectral fluctuations of the energy spectrum. The level spacing distribution $P(s)$ as well the Dyson-Mehta statistics…
Phase transitions are prevalent throughout physics, spanning thermal phenomena like water boiling to magnetic transitions in solids. They encompass cosmological phase transitions in the early universe and the transition into a quark-gluon…
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 study the metal-insulator transition in a tight-binding one-dimensional (1D) model with long-range correlated disorder. In the case of diagonal disorder with site energy within $[-\frac{W}{2},\frac{W}{2}]$ and having a power-law spectral…
We report a new attractive critical point occurring in the Anderson localization scaling flow of symplectic models on fractals. The scaling theory of Anderson localization predicts that in disordered symplectic two-dimensional systems weak…
We investigate, by numerically calculating the charge stiffness, the effects of random diagonal disorder and electron-electron interaction on the nature of the ground state in the 2D Hubbard model through the finite size exact…
The interplay between strong Coulomb interactions and randomness has been a long-standing problem in condensed matter physics. According to the scaling theory of localization, in two-dimensional systems of noninteracting or weakly…
Quantum phase transitions are typically marked by changes in quantum correlations across various spatial scales within the system. A key challenge lies in the fact that experimental probes are generally restricted to diagonal quantities at…
The single-parameter scaling hypothesis predicts the absence of delocalized states for noninteracting quasiparticles in low-dimensional disordered systems. We show analytically and numerically that extended states may occur in the one- and…
We study the hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by…
We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the non-local correlation effects induced by disorder on the density of states…
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…
At low temperature T, a significant difference between the behavior of crystals on the one hand and disordered solids on the other is seen: sufficiently strong disorder can give rise to a transition of the transport properties from…
We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one-dimension: the dynamical exponent is infinite and,…
Experimental evidence for the possible universality classes of the metal-insulator transition (MIT) in two dimensions (2D) is discussed. Sufficiently strong disorder, in particular, changes the nature of the transition. Comprehensive…
We uncover a disorder-driven instability in the diffusive Fermi liquid phase of a class of many-fermion systems, indicative of a metal-insulator transition of first order type, which arises solely from the competition between quenched…
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…
A wide variety of complex systems exhibit large fluctuations both in space and time that often can be attributed to the presence of some kind of critical phenomena. Under such critical scenario it is well known that the properties of the…
We investigate localization properties of electron eigenstates in one-dimensional (1d) systems with long-range correlated diagonal disorder. Numerical studies on the localization length $\xi$ of eigenstates demonstrate the existence of the…