Symmetries of multifractal spectra and field theories of Anderson localization

Abstract

We uncover field-theoretic underpinnings of symmetry relations for multifractal spectra at Anderson transitions and at critical points of other disordered systems. We show that such relations follow from the conformal invariance of the critical theory, which implies their general character. We also demonstrate that for the Anderson localization problem the entire probability distribution for the local density of states possesses a symmetry arising from the invariance of correlation functions of the underlying non-linear $\sigma$-model with respect to the Weyl group of the target space of the model.

Published version

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Cited by in corpus (31)

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• The integer quantum Hall plateau transition is a current algebra after all
• Multifractality at Anderson transitions with Coulomb interaction
• 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
• Localization transition in one dimension using Wegner flow equations
• Multifractal dimensions for all moments for certain critical random matrix ensembles in the strong multifractality regime
• Gaussian free fields at the integer quantum Hall plateau transition
• The Renyi Entropy and the Multifractal Spectrum of Systems Near the Localization Transition
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• Multifractality and electron-electron interaction at Anderson transitions
• Pure scaling operators at the integer quantum Hall plateau transition
• Many-body Localization Transition in Rokhsar-Kivelson-type wave functions
• Quartic multifractality and finite-size corrections at the spin quantum Hall transition
• Generalized multifractality at spin quantum Hall transition
• Generalized multifractality at metal-insulator transitions and in metallic phases of 2D disordered systems
• Integration on Non-Compact Supermanifolds
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• Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
• Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
• Statistics of Conductances and Subleading Corrections to Scaling near the Integer Quantum Hall Plateau Transition
• Generalized surface multifractality in 2D disordered systems
• Generalized multifractality in the spin quantum Hall symmetry class with interaction
• Multifractality in monitored single-particle dynamics
• Quantum logarithmic multifractality
• Statistics of a simple transmission mode on a lossy chaotic background
• Boundary multifractality in the spin quantum Hall symmetry class with interaction
• Generalized multifractality at the spin quantum Hall transition: Percolation mapping and pure-scaling observables