Symmetries of multifractal spectra and field theories of Anderson localization

Details Symmetries of multifractal spectra and field theories of Anderson localization Symmetries of multifractal spectra and field theories of Anderson localization

2011-03-23

arxiv.org/abs/1103.4627v2

Phys. Rev. Lett. 107:086403,2011

Physics

Condensed Matter

Disordered Systems and Neural Networks

Published version

Scientific paper

10.1103/PhysRevLett.107.086403

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.

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