Related papers: Critical behavior at the integer quantum Hall tran…
We investigate the critical behavior of three-dimensional ferromagnetic CP(N-1) models, which are characterized by a global U(N) and a local U(1) symmetry. We perform numerical simulations of a lattice model for N=2, 3, and 4. For N=2 we…
Generic classical electron motion in a strong perpendicular magnetic field and random potential reduces to the bond percolation on a square lattice. Here we point out that for certain smooth 2D potentials with 120 degrees rotational…
We calculated numerically the localization length index $\nu$ for the Chalker-Coddington model of the plateau-plateau transitions in the quantum Hall effect. By taking into account finite size effects we have obtained $\nu = 2.593 \pm…
I investigate the Kazakov-Migdal (KM) model -- the Hermitean gauge-invariant matrix model on a D-dimensional lattice. I utilize an exact large-N solution of the KM model with a logarithmic potential to examine its critical behavior. I find…
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 consider localisation problems belonging to the chiral symmetry classes, in which sublattice symmetry is responsible for singular behaviour at a band centre. We formulate models which have the relevant symmetries and which are…
We study rigidity percolation transitions in two-dimensional central-force isostatic lattices, including the square and the kagome lattices, as next-nearest-neighbor bonds ("braces") are randomly added to the system. In particular, we focus…
A two-dimensional lattice model for non-interacting fermions in a magnetic field with half a flux quantum per plaquette and $N$ levels per site is considered. This is a model which exhibits the Integer Quantum Hall Effect (IQHE) in the…
A critical dilute O($n$) model on the kagome lattice is investigated analytically and numerically. We employ a number of exact equivalences which, in a few steps, link the critical O($n$) spin model on the kagome lattice to the exactly…
One-dimensional (1D) systems and models provide a versatile platform for emergent phenomena induced by strong electron correlation. In this work, we extend the newly developed real space neural network quantum Monte Carlo methods to study…
We study a number of hierarchical network models related to the Chalker-Coddington model of quantum percolation. Our aim is to describe the physics of the quantum Hall transition. The hierarchical network models are constructed by combining…
We report results of numerical studies of the integer quantum Hall effect in a tight binding model on a two-dimensional square lattice with non-interacting electrons, in the presence of a random potential as well as a uniform magnetic field…
Recent experimental discovery of several families of kagome-lattice materials has boosted the interest in electronic correlations on kagome lattice. As an initial step to understand the observed complex phenomena, it is helpful to know the…
A model consisting of a mixture of superconducting and quantum links is proposed to describe the integer quantum Hall transition. The quantum links correspond to tunneling of electrons between trajectories trapped in adjacent potential…
The critical behavior of a dimer model with an interaction favoring parallel dimers in each plaquette of the square lattice is studied numerically by means of the Corner Transfer Matrix Renormalization Group algorithm. The critical…
A three-dimensional elemental carbon Kagome lattice (CKL), made of only fourfold coordinated carbon atoms, is proposed based on first-principles calculations. Despite the existence of 60{\deg} bond angles in the triangle rings, widely…
We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a…
We consider a network model, embedded on the Manhattan lattice, of a quantum localisation problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are…
At the quantum critical point of correlated materials, a non-Fermi liquid state appears where electron correlations continuously develop to very low temperatures. The relaxation time of the interacted electrons, namely quasiparticles, is…
The synchronization of oscillator ensembles is pervasive throughout nonlinear science, from classical or quantum mechanics to biology, to human assemblies. Traditionally, the main focus has been the identification of threshold parameter…