Random network models and quantum phase transitions in two dimensions

  title={Random network models and quantum phase transitions in two dimensions},
  author={Bernhard K. Kramer and Tomi Ohtsuki and Stefan Kettemann},
  journal={Physics Reports},
Geometry of random potentials: Induction of two-dimensional gravity in quantum Hall plateau transitions
Integer quantum Hall plateau transitions are usually modeled by a system of noninteracting electrons moving in a random potential. The physics of the most relevant degrees of freedom, the edge
Localization-length exponent in two models of quantum Hall plateau transitions
Motivated by the recent numerical studies on the Chalker-Coddington network model that found a larger-than-expected critical exponent of the localization length characterizing the integer quantum
Anderson transitions on random Voronoi-Delaunay lattices
The dissertation covers phase transitions in the realm of the Anderson model of localization on topologically disordered Voronoi-Delaunay lattices. The disorder is given by random connections which
Topological phase transitions in glassy quantum matter
Amorphous systems have rapidly gained promise as novel platforms for topological matter. In this work we establish a scaling theory of amorphous topological phase transitions driven by the density of
Spin-mixing-tunneling network model for Anderson transitions in two-dimensional disordered spinful electrons
We consider Anderson transitions in two-dimensional spinful electron gases subject to random scalar potentials with time-reversal-symmetric spin-mixing tunneling (SMT) and spin-preserving tunneling
Proposal for realizing anomalous Floquet insulators via Chern band annihilation
Two-dimensional periodically driven systems can host an unconventional topological phase unattainable for equilibrium systems, termed the Anomalous Floquet-Anderson insulator (AFAI). The AFAI
The quantum Hall effect in narrow quantum wires
The quantum phase diagram of disordered quantum wires in a strong magnetic field is reviewed. For uncorrelated disorder potential the 2‐terminal conductance, as calculated with the numerical transfer
The quantum percolation model of the scaling theory of the quantum Hall effect: a unifying model for plateau-to-plateau transitions
We present a unifying model of plateau-to-plateau transitions in the quantum Hall effect based on results from high resolution frequency scaling experiments. We show that as the frequency or quantum
Quantum transport and non-unitary gauge invariance in graphene-based electronic systems
Quantum transport is studied in electronic two-terminal devices with monoand few-layer graphene samples described by the low-energy effective theories. Using the scattering approach, the full


Two-dimensional random-bond Ising model, free fermions, and the network model
We develop a recently proposed mapping of the two-dimensional Ising model with random exchange (RBIM) via the transfer matrix, to a network model for a disordered system of noninteracting fermions.
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 and classical localization, the spin quantum Hall effect, and generalizations
We consider network models for localization problems belonging to symmetry class C. This symmetry class arises in a description of the dynamics of quasiparticles for disordered spin-singlet
Toward a theory of the integer quantum Hall transition: Continuum limit of the Chalker–Coddington model
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
Network models for localization problems belonging to the chiral symmetry classes
We consider localization problems belonging to the chiral symmetry classes, in which sublattice symmetry is responsible for singular behavior at a band center. We formulate models that have the
Scaling and crossover functions for the conductance in the directed network model of edge states
We consider the directed network (DN) of edge states on the surface of a cylinder of length L and circumference C .B y mapping it to a ferromagnetic superspin chain, and using a scaling analysis, we
Point-contact conductances at the quantum Hall transition
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
Connecting polymers to the quantum Hall plateau transition
A mapping is developed between the quantum Hall plateau transition and two-dimensional self-interacting lattice polymers. This mapping is exact in the classical percolation limit of the plateau
Random-matrix theory of quantum transport
This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot is a confined
Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
When the two-dimensional random-bond Ising model is represented as a noninteracting fermion problem, it has the same symmetries as an ensemble of random matrices known as class D. A nonlinear sigma