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

• URL: http://arxiv.org/abs/2603.15290v1
• Date: Mon, 16 Mar 2026 13:52:41 GMT
• Title: Extreme-Value Criticality and Gain Decomposition at the Integer Quantum Hall Transition
• Abstract summary: We show that the maximal wave-function amplitude separates into a global gain and an intrinsic extreme component.<n>Extreme observables provide a robust probe of correlated criticality in open quantum systems.
• Score: 6.416957991576607
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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, $|ψ|_{\max}=A\,|\tildeψ|_{\max}$. We introduce extreme-moment scaling for $|ψ|_{\max}$ and observe an approximately parabolic exponent function $τ_{\max}(q)$ over moderate $q$, while $\ln|ψ|_{\max}$ 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: $\tildeτ_{\max}(q)$ changes qualitatively and $|\tildeψ|_{\max}$ 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.

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