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, $|\ddot{I}ˆ{|}_{\max }=A|\tilde{\ddot{I}}ˆ{|}_{\max }$. We introduce extreme-moment scaling for $|\ddot{I}ˆ{|}_{\max }$ and observe an approximately parabolic exponent function $\ddot{I}{„}_{\max }(q)$ over moderate $q$, while $\ln |\ddot{I}ˆ{|}_{\max }$ 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: $\tilde{\ddot{I}}{„}_{\max }(q)$ changes qualitatively and $|\tilde{\ddot{I}}ˆ{|}_{\max }$ 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