Puschmann, Martin 
; Hernangómez-Pérez, Daniel ; Lang, Bruno ; Bera, Soumya ; Evers, Ferdinand
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Quartic multifractality and finite-size corrections at the spin quantum Hall transition. (Eingebracht am 08 Jun 2021 05:47)
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Zusammenfassung
The spin-quantum Hall (or class C) transition represents one of the few localization-delocalization transitions for which some of the critical exponents are known exactly. Not known, however, is the multifractal spectrum, $\tau_q$, which describes the system-size scaling of inverse participation ratios $P_q$, i.e., the $q$-moments of critical wavefunction amplitudes. We here report simulations ...
Zusammenfassung
The spin-quantum Hall (or class C) transition represents one of the few localization-delocalization transitions for which some of the critical exponents are known exactly. Not known, however, is the multifractal spectrum, 
, which describes the system-size scaling of inverse participation ratios 
, i.e., the 
-moments of critical wavefunction amplitudes. We here report simulations based on the class C Chalker-Coddington network and demonstrate that is (essentially) a quartic polynomial in . Analytical results fix all prefactors except the quartic curvature that we obtain as 
. In order to achieve the necessary accuracy in the presence of sizable corrections to scaling, we have analyzed the evolution with system size of the entire -distribution function. As it turns out, in a sizable window of -values this distribution function exhibits a (single-parameter) scaling collapse already in the pre-asymptotic regime, where finite-size corrections are {
not} negligible. This observation motivates us to propose a novel approach for extracting based on concepts borrowed from the Kolmogorov-Smirnov test of mathematical statistics. We believe that our work provides the conceptual means for high-precision investigations of multifractal spectra also near other localization-delocalization transitions of current interest, especially the integer (class A) quantum Hall effect.
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