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  • Letter
  • Open Access

Extreme-value criticality and gain decomposition at the integer quantum Hall transition

Wei-Han Li* and Abbas Ali Saberi†

  • *Contact author: wei-han.li@outlook.com
  • †Contact author: asaberi@constructor.university
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Phys. Rev. B 113, L241108 – Published 4 June, 2026

DOI: https://doi.org/10.1103/wzs6-3s61

Abstract

Extreme-value fluctuations at quantum critical points remain poorly understood in the presence of strong correlations and open-system amplification. We study the maximum wave-function amplitude in the open Chalker-Coddington network at the integer quantum Hall transition. Because the stationary scattering state is not normalized to unit total intensity, its largest amplitude contains both a sample-dependent global intensity scale and an intrinsic spatial extreme. We separate these contributions by writing the state as a total gain times a normalized spatial pattern. The raw maximum shows near-log-normal statistics over the studied sizes and an approximately parabolic extreme-moment exponent in a moderate moment window. We show that this behavior is strongly shaped by the fluctuating gain. After gain normalization, the maximum has a qualitatively different exponent function and does not collapse to a standard generalized extreme-value form under the same centering and scaling. These results identify extreme amplitudes as sensitive probes of open quantum criticality and separate collective amplification from intrinsic rare-event fluctuations.

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Outline

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Phys. Rev. B 113, L241108– Published 4 June, 2026
  • Received 4 March 2026
  • Revised 13 May 2026
  • Accepted 19 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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