Generalized surface multifractality in twodimensional disordered systems
Abstract
Recently, a concept of generalized multifractality, which characterizes fluctuations and correlations of critical eigenstates, was introduced and explored for all 10 symmetry classes of disordered systems. Here, by using the nonlinear sigmamodel (NL σ M ) field theory, we extend the theory of generalized multifractality to boundaries of systems at criticality. Our numerical simulations on twodimensional systems of symmetry classes A, C, and AII fully confirm the analytical predictions of purescaling observables and Weyl symmetry relations between critical exponents of surface generalized multifractality. This demonstrates the validity of the NL σ M for the description of Andersonlocalization critical phenomena, not only in the bulk but also on the boundary. The critical exponents strongly violate generalized parabolicity, in analogy with earlier results for the bulk, corroborating the conclusion that the considered Andersonlocalization critical points are not described by conformal field theories. We further derive relations between generalized surface multifractal spectra and linear combinations of Lyapunov exponents of a strip in quasionedimensional geometry, which hold under the assumption of invariance with respect to a logarithmic conformal map. Our numerics demonstrate that these relations hold with an excellent accuracy. Taken together, our results indicate an intriguing situation: the conformal invariance is broken but holds partially at critical points of Anderson localization.
 Publication:

Physical Review B
 Pub Date:
 September 2023
 DOI:
 10.1103/PhysRevB.108.104205
 arXiv:
 arXiv:2306.09455
 Bibcode:
 2023PhRvB.108j4205B
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Mathematical Physics
 EPrint:
 19 pages, 21 figures