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• W3177453192 abstract "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 based on the class C Chalker-Coddington network and demonstrate that $tau_q$ is (essentially) a quartic polynomial in $q$. Analytical results fix all prefactors except the quartic curvature that we obtain as $gamma=(2.22pm{0.15})cdot10^{-3}$. 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 $P_q$-distribution function. As it turns out, in a sizable window of $q$-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 $tau_q$ 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." @default.
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• W3177453192 date "2021-06-30" @default.
• W3177453192 modified "2023-10-16" @default.
• W3177453192 title "Quartic multifractality and finite-size corrections at the spin quantum Hall transition" @default.
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• W3177453192 doi "https://doi.org/10.1103/physrevb.103.235167" @default.
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