Padayasi Jaychandran, Gruzberg Ilya
Department of Physics, Ohio State University, 191 West Woodruff Avenue, Columbus, Ohio 43210, USA.
Phys Rev Lett. 2023 Dec 29;131(26):266401. doi: 10.1103/PhysRevLett.131.266401.
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.
多重分形出现在自然界的各种系统中，其标度行为由连续的多重分形指数Δₑ表征。在安德森转变的背景下，临界波函数的多重分形性在转变的场论描述中由具有标度维度Δₑ的算符Oₑ描述。算符Oₑ满足所谓的阿贝尔融合，表现为简单的算符乘积展开。假设共形不变性和阿贝尔融合，我们使用共形引导框架来推导一个约束条件，该条件意味着在任何维度d≥2中多重分形谱Δₑ（及其广义形式）在其自变量中必须是二次的。
