Logarithmic Correlations in Quantum Hall Plateau Transitions

Abstract

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 origin of these logarithmic correlation functions remain however mysterious. Using the replica trick and the underlying symmetries of these quantum critical points, we show here how to construct non-perturbatively disorder-averaged observables in terms of Green's functions that scale logarithmically at criticality. In the case of the spin quantum Hall transition, which may occur in disordered superconductors with spin-rotation symmetry and broken time reversal invariance, we argue that our results are compatible with an alternative approach based on supersymmetry. The generalization to the Integer quantum Hall plateau transition is also discussed.

18 pages, 5 figures. v3: Published version

References in corpus (8)

• Associative-algebraic approach to logarithmic conformal field theories
• Enlarged symmetry algebras of spin chains, loop models, and S-matrices
• From Percolation to Logarithmic Conformal Field Theory
• Virasoro representations and fusion for general augmented minimal models
• Logarithmic observables in critical percolation
• Logarithmic M(2,p) Minimal Models, their Logarithmic Couplings, and Duality
• Boundary criticality and multifractality at the 2D spin quantum Hall transition
• The periodic sl(2|1) alternating spin chain and its continuum limit as a bulk Logarithmic Conformal Field Theory at c=0

Cited by in corpus (1)

• Gaussian free fields at the integer quantum Hall plateau transition