Extreme-Value Criticality and Gain Decomposition at the Integer Quantum Hall Transition

Abstract

Extreme-value fluctuations at quantum critical points remain poorly understood in the presence of strong correlations and openness. At the integer quantum Hall transition in the open Chalker--Coddington network, we show that the maximal wave-function amplitude separates into a global gain and an intrinsic extreme component, $|\psi {|}_{\max }=A|\tilde{\psi }{|}_{\max }$. We introduce extreme-moment scaling for $|\psi {|}_{\max }$ and observe an approximately parabolic exponent function ${\tau }_{\max }(q)$ over moderate $q$, while $\ln |\psi {|}_{\max }$ displays an almost Gaussian bulk over the studied sizes. The gain factor is close to log-normal and largely controls the raw extremes. Gain normalization reorganizes the statistics: ${\tilde{\tau }}_{\max }(q)$ changes qualitatively and $|\tilde{\psi }{|}_{\max }$ does not support a single-parameter generalized extreme-value collapse under standard centering/scaling in the accessible size window. Extreme observables thus provide a robust probe of correlated criticality in open quantum systems.

8 pages, 8 figures

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