【报告题目】: Dual-Space Invariance as a Universal Criterion for Multifractal Critical States
【报告人】 ：刘通，南京邮电大学
【报告时间】：3月4日，10:00-12:00
【报告地点】：29幢414
【报告摘要】：In Anderson localization, eigenstates of disordered quantum systems are broadly classified as extended, localized, or critical. Although critical states exhibit multifractal character, a precise and operational criterion for their identification remains an open challenge, as Lyapunov exponents in real space cannot uniquely distinguish them from extended states. Here we address this challenge by asserting that critical states are uniquely characterized by an emergent dual-space invariance between position and momentum space. Building on the Liu--Xia criterion of the simultaneous vanishing of Lyapunov exponents ($\gamma=\gamma_m=0$), we show that this dual-space invariance extends beyond Lyapunov exponents and governs wavefunction scaling, revealing a fundamental property inaccessible from either space alone. Through numerical simulations, we demonstrate that the inverse participation ratio exhibits matching scaling behavior in position and momentum space for critical states, in sharp contrast to extended and localized states, which display a pronounced asymmetry between the two spaces. This dual-space invariance provides a direct, robust, and universal criterion for identifying multifractal critical states. Our results establish a fundamental principle of Anderson criticality and open new avenues for its detection in modern quantum simulation platforms.
【报告人简介】：刘通博士，南京邮电大学教师，主要从事安德森局域化及多体局域化的理论研究，相关成果发表于Physical Review 等国际SCI期刊，已发表学术论文二十余篇。
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