Extreme-Value Criticality and Gain Decomposition at the Integer Quantum Hall Transition
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| Format: | Preprint |
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2026
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| _version_ | 1866918391376248832 |
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| author | Li, Wei-Han Saberi, Abbas Ali |
| author_facet | Li, Wei-Han Saberi, Abbas Ali |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_15290 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extreme-Value Criticality and Gain Decomposition at the Integer Quantum Hall Transition Li, Wei-Han Saberi, Abbas Ali Disordered Systems and Neural Networks Statistical Mechanics Data Analysis, Statistics and Probability Quantum Physics 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. |
| title | Extreme-Value Criticality and Gain Decomposition at the Integer Quantum Hall Transition |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Data Analysis, Statistics and Probability Quantum Physics |
| url | https://arxiv.org/abs/2603.15290 |