Conformal invariance and multifractality at Anderson transitions in arbitrary dimensions

Author:

Jaychandran Padayasi, Ilya A. Gruzberg

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), High Energy Physics - Theory (hep-th)

journal:

date:

2023-06-11 16:00:00

Abstract

Electronic wave functions at Anderson transitions exhibit multifractal scaling characterized by a continuum of generalized multifractal exponents $\Delta_\gamma$ with vector indices $\gamma = (q_1,\ldots,q_n)$. In a field theory description of the transitions, there are corresponding multifractal operators $\mathcal{O}_\gamma$ with scaling dimensions $\Delta_\gamma$. Assuming conformal invariance and using the conformal bootstrap framework, we derive a constraint that implies that the generalized multifractal spectrum $\Delta_\gamma$ must be quadratic in all $q_i$ in any dimension $d > 2$. As several numerical studies have shown deviations from parabolicity, we argue that conformal invariance is likely absent at Anderson transitions in dimensions $d > 2$.

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