Papers › Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
Jaychandran Padayasi, Ilya A. Gruzberg
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Multifractals arise in various systems across nature whose scaling behavior is characterized by a continuous spectrum of multifractal exponents Δ_q. In the context of Anderson transitions, the multifractality of critical wave functions is described by operators O_q with scaling dimensions Δ_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 Δ_q (and its generalized form) must be quadratic in its arguments in any dimension d ≥2.
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