Wave function multifractality and dephasing at metal-insulator and quantum Hall transitions

Abstract

We analyze the critical behavior of the dephasing rate induced by short-range electron-electron interaction near an Anderson transition of metal-insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in $2+\epsilon$ dimensions) with numerical simulations on the Chalker-Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data.

33 pages, 7 figures, elsart style

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Cited by in corpus (25)

• Enhancement of superconductivity by Anderson localization
• Statistics of eigenstates near the localization transition on random regular graphs
• Classification and symmetry properties of scaling dimensions at Anderson transitions
• Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions
• Finite Size Scaling of the Chalker-Coddington Model
• Integer quantum Hall transition on a tight-binding lattice
• Scaling Behavior of the Quantum Phase Transition from a Quantum Anomalous Hall Insulator to an Axion Insulator
• Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way
• Random network models with variable disorder of geometry
• Coherent backscattering reveals the Anderson transition
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• Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems
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• Generalized surface multifractality in 2D disordered systems
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Mesoscopic fluctuations of the local density of states in interacting electron systems
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• Quantum Hall criticality in an amorphous Chern insulator
• Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models