Related papers: Spin quantum Hall transition on random networks: e…
We study relevant perturbations at the spin quantum Hall critical point using a network model formulation. The model has been previously mapped to classical percolation on a square lattice, and we use the mapping to extract exact analytical…
Critical properties of quantum Hall systems are affected by the presence of extra edge channels - present, in particular, at higher plateau transitions. We study this phenomenon for the case of the spin quantum Hall transition. Using…
A review is given of quantum network models in class C which, on a suitable 2d lattice, describe the spin quantum Hall plateau transition. On a general class of graphs, however, many observables of such models can be mapped to those of a…
We reduce the problem of integer quantum Hall transition to a random rotation of an N-dimensional vector by an su(N) algebra, where only N specially selected generators of the algebra are nonzero. The group-theoretical structure revealed in…
We consider the spin quantum Hall transition which may occur in disordered superconductors with unbroken SU(2) spin-rotation symmetry but broken time-reversal symmetry. Using supersymmetry, we map a model for this transition onto 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…
In this paper we propose a new $S$-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work 10.1103/PhysRevB.95.125414. Random networks are modifications of the…
We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups $U(N)$, $O(N)$ and…
We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry…
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 consider the network model of the integer quantum Hall effect transition. By generalizing the real--space renormalization group procedure for the classical percolation to the case of quantum percolation, we derive a closed…
We study localization-delocalization transition in quantum Hall systems with a random field of nuclear spins acting on two-dimensional (2d) electron spins via hyperfine contact (Fermi) interaction. We use Chalker-Coddington network model,…
We consider transitions in quantum networks analogous to those in the two-dimensional Ising model. We show that for a network of active components the transition is between the quantum and the classical behaviour of the network, and the…
The critical behavior of quantum Hall transitions in two-dimensional disordered electronic systems can be described by a class of complicated, non-unitary conformal field theories with logarithmic correlations. The nature and the physical…
We study the quantum Hall transition using the density-density correlation function. We show that in the limit h->0 the electron density moves along the percolating trajectories, undergoing normal diffusion. The localization exponent…
We review some elementary aspects of the critical properties of the series of metal-insulator transitions that constitute the integer quantum Hall effect. Numerical work has proven essential in charting out this phenomenon. Without being…
An overview of the random network model invented by Chalker and Coddington, and its generalizations, is provided. After a short introduction into the physics of the Integer Quantum Hall Effect, which historically has been the motivation for…
We study the localization transition in the integer quantum Hall effect as described by the network model of quantum percolation. Starting from a path integral representation of transport Green's functions for the network model, which…
The integer quantum Hall transition (IQHT) is one of the most mysterious members of the family of Anderson transitions. Since the 1980s, the scaling behavior near the IQHT has been vigorously studied in experiments and numerical…
We address the geometrical critical behavior of the two-dimensional Q-state Potts model in terms of the spin clusters (i.e., connected domains where the spin takes a constant value). These clusters are different from the usual…