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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Li, Wei-Han, Saberi, Abbas Ali
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918391376248832
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
id 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