Gaussian free fields at the integer quantum Hall plateau transition

Abstract

In this work we put forward an effective Gaussian free field description of critical wavefunctions at the transition between plateaus of the integer quantum Hall effect. To this end, we expound our earlier proposal that powers of critical wave intensities prepared via point contacts behave as pure scaling fields obeying an Abelian operator product expansion. Our arguments employ the framework of conformal field theory and, in particular, lead to a multifractality spectrum which is parabolic. We also derive a number of old and new identities that hold exactly at the lattice level and hinge on the correspondence between the Chalker-Coddington network model and a supersymmetric vertex model.

48 pages, 4 figures

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Cited by in corpus (22)

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• Numerical evidence for marginal scaling at the integer quantum Hall transition
• Quantum Hall criticality in Floquet topological insulators
• Marginal CFT perturbations at the integer quantum Hall transition
• Quartic multifractality and finite-size corrections at the spin quantum Hall transition
• Generalized multifractality at spin quantum Hall transition
• Numerical Study of a Dual Representation of the Integer Quantum Hall Transition
• Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
• Generalized surface multifractality in 2D disordered systems
• Generalized multifractality in the spin quantum Hall symmetry class with interaction
• Effect of Hilbert space truncation on Anderson localization
• Composite Fermion Nonlinear Sigma Models
• On truncations of the Chalker-Coddington model
• Critical behavior at the integer quantum Hall transition in a network model on the Kagome lattice
• Topology and many-body localization
• Irrelevant corrections at the quantum Hall transition
• Quantum Hall criticality in an amorphous Chern insulator
• Instanton analysis for the spin quantum Hall symmetry class: Non-perturbative corrections to physical observables and generalized multifractal spectrum
• Boundary multifractality in the spin quantum Hall symmetry class with interaction