Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions

Abstract

Multifractals arise in various systems across nature whose scaling behavior is characterized by a continuous spectrum of multifractal exponents ${\Delta }_q$. In the context of Anderson transitions, the multifractality of critical wave functions is described by operators $O_q$ with scaling dimensions ${\Delta }_q$ in a field-theory description of the transitions. The operators $O_q$ satisfy the so-called Abelian fusion expressed as a simple operator product expansion. Assuming conformal invariance and Abelian fusion, we use the conformal bootstrap framework to derive a constraint that implies that the multifractal spectrum ${\Delta }_q$ (and its generalized form) must be quadratic in its arguments in any dimension $d\ge 2$.

arXiv commentPublished version

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• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Multifractality in monitored single-particle dynamics
• Instanton analysis for the spin quantum Hall symmetry class: Non-perturbative corrections to physical observables and generalized multifractal spectrum
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Conformal invariance in out-of-equilibrium Bose-Einstein condensates governed by the Gross-Pitaevskii Equation