Network Models of Quantum Percolation and Their Field-Theory Representations

Abstract

We obtain the field-theory representations of several network models that are relevant to 2D transport in high magnetic fields. Among them, the simplest one, which is relevant to the plateau transition in the quantum Hall effect, is equivalent to a particular representation of an antiferromagnetic SU(2N) ($N\to 0$) spin chain. Since the later can be mapped onto a $\theta \ne 0$, $U(2N)/U(N)\times U(N)$ sigma model, and since recent numerical analyses of the corresponding network give a delocalization transition with $\nu \approx 2.3$, we conclude that the same exponent is applicable to the sigma model.

Cited by in corpus (45)

• Anderson Transitions
• Interacting topological insulators: a review
• Topological Materials Discovery from Crystal Symmetry
• Random Network Models and Quantum Phase Transitions in Two Dimensions
• Wire deconstructionism of two-dimensional topological phases
• Network Models of Photonic Floquet Topological Insulators
• Models for the integer quantum Hall effect: the network model, the Dirac equation, and a tight-binding Hamiltonian
• Toward a theory of the integer quantum Hall transition: continuum limit of the Chalker-Coddington model
• Quantum Spin Hall Effect in Strip of Stripes Model
• Field theory of compact polymers on the square lattice
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect
• Integer and Fractional Quantum Hall Effect in a Strip of Stripes
• Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
• Helical nuclear spin order in a strip of stripes in the Quantum Hall regime
• Wire constructions of Abelian topological phases in three or more dimensions
• Relating c<0 and c>0 Conformal Field Theories
• Localization in the quantum Hall regime
• Coupled-wire constructions: a Luttinger liquid approach to topology
• Recovery of massless Dirac fermions at charge neutrality in strongly interacting twisted bilayer graphene with disorder
• Spin-directed network model for the surface states of weak three-dimensional ${\mathbb{Z}}_2^{}$ topological insulators
• Calculation of the conductance of a graphene sheet using the Chalker-Coddington network model
• Effect of spin degeneracy on scaling in the quantum Hall regime
• Localization length index in a Chalker-Coddington model: a numerical study
• Ground state degeneracy of non-Abelian topological phases from coupled wires
• Duality and Universality for the Chern-Simons bosons
• On a Network Model of Localization in a Random Magnetic Field
• Edge states of integral quantum Hall states versus edge states of antiferromagnetic quantum spin chains
• Quantum Hall network models as Floquet topological insulators
• Integer Quantum Hall Effect in Double-Layer Systems
• From Disordered Quantum Walk to Physics of Off-diagonal Disorder
• Effective Floquet model for minimally twisted bilayer graphene
• Weakly chiral networks and 2D delocalized states in a weak magnetic field
• Self-duality of the integer quantum Hall to insulator transition: composite fermion description
• Real-space renormalization-group approach to the integer quantum Hall effect
• Asymptotic behavior of the conductance in disordered wires with perfectly conducting channels
• Transport in tight-binding bond percolation models
• Disordered Weyl semimetal as an array of coupled Hubbard chains
• Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully non-universal
• Supersymmetry on a lattice and Dirac fermions in a random vector potential
• The superspin approach to a disordered quantum wire in the chiral-unitary symmetry class with an arbitrary number of channels
• Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models
• Random Magnetic Field and the Dirac Fermi Surface
• Fermions in an anisotropic random magnetic field
• Supermetal-insulator transition in a non-Hermitian network model