Related papers: Random Network Models and Quantum Phase Transition…
It is the purpose of the present article to show that so-called network models, originally designed to describe static properties of disordered electronic systems, can be easily generalized to quantum-{\em dynamical} models, which then…
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 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…
An N-channel generalization of the network model of Chalker and Coddington is considered. The model for N = 1 is known to describe the critical behavior at the plateau transition in systems exhibiting the integer quantum Hall effect. Using…
The Chalker-Coddington network model is often used to describe the transport properties of quantum Hall systems. By adding an extra channel to this model, we introduce an asymmetric model with profoundly different transport properties. We…
We show that the localization transition in the integer quantum Hall effect as described by the Chalker-Coddington network model is quantum critical. We first map the anisotropic network model to the problem of diagonalizing a…
We construct a three-dimensional (3D), time-reversal symmetric generalization of the Chalker-Coddington network model for the integer quantum Hall transition. The novel feature of our network model is that in addition to a weak topological…
The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced.…
We study hierarchical network models which have recently been introduced to approximate the Chalker-Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 56 1422 (1997); Arovas et al., PRB 56, 4751 (1997)).…
The effects of static disorder on the Z_2 quantum spin-Hall effect for non-interacting electrons propagating in two-dimensional space is studied numerically. A two-dimensional time-reversal symmetric network model is constructed to account…
Recently it was shown (I.A.Gruzberg, A. Kl\"umper, W. Nuding and A. Sedrakyan, Phys.Rev.B 95, 125414 (2017)) that taking into account random positions of scattering nodes in the network model with $U(1)$ phase disorder yields a localization…
We numerically investigate the influence of classical percolation on the quantum Hall localization-delocalization transition. This is accomplished within the framework of the generalized Chalker--Coddington network model which allows us to…
On the basis of the Chalker-Coddington network model, a numerical and analytical study is made of the statistics of point-contact conductances for systems in the integer quantum Hall regime. In the Hall plateau region the point-contact…
We study a quantum network percolation model which is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We show dynamical localization for parameters corresponding to edges of Landau…
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…
Percolation theory allows simple description of the phase transition based on the scaling properties of the network clusters with respect to a single parameter - site or bond occupation probability. How to design a network exhibiting the…
The interplay of geometric randomness and strong quantum fluctuations is an exciting topic in quantum many-body physics, leading to the emergence of novel quantum phases in strongly correlated electron systems. Recent investigations have…
Quantum communication demands efficient distribution of quantum entanglement across a network of connected partners. The search for efficient strategies for the entanglement distribution may be based on percolation theory, which describes…
A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional…
Effective-medium theory is applied to the percolation description of the metal-insulator transition in two dimensions with emphasis on the continuous connection between the zero-magnetic-field transition and the quantum Hall transition. In…