具有长程跃迁的一维系统中的半局域基态
Semi-localized ground state in a 1D system with long-range hopping
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中文总结 AI 辅助
该研究探讨长程跃迁一维系统中量子粒子的局域化，发现$1<a<3/2$时带边存在无序驱动相变，基态呈半局域化，扩展了半分形波函数模型类别。
中文摘要 AI 辅助
我们研究量子粒子在具有长程跃迁振幅$t(r)\propto r^{-a}$的一维无序系统中的局域化问题。与标准一维安德森模型（$a\to\infty$，所有态均局域化且带边处局域化长度最小）不同，$1<a<3/2$的长程模型在带边处存在无序驱动的相变，而高能态在任意无序强度下均保持局域化。我们在动量空间中研究基态的这一相变，在弱无序 regime 下推导动量空间波函数的特征函数、矩及其分形维数的微扰表达式。结果表明，该基态呈现半局域化而非传统局域化，从而扩展了显示波函数异常半分形性的模型类别。
英文摘要
We study the localization of a quantum particle in a one-dimensional disordered system with long-range hopping amplitudes $t(r)\propto r^{-a}$. In contrast to the standard one-dimensional Anderson model ($a\to\infty$), in which all states are localized and the localization length is minimal at the band edge, the long-range model with $1<a<3/2$ exhibits a disorder-driven transition at the band edge, while high-energy states remain localized at arbitrary disorder strength. We investigate this transition for the ground state in momentum space. In the weak-disorder regime, we derive perturbative expressions for the characteristic functions and moments of the momentum-space wave function, as well as for its fractal dimensions. Our results demonstrate that the ground state exhibits $\it semilocalization$ rather than conventional localization, thereby extending the class of models displaying the unusual $\it semifractality$ of wave functions.
发表机构
- Russian Quantum Center（俄罗斯量子中心）
- National Research University Higher School of Economics（国立高等经济大学）
- Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）
- ICTP（理论物理中心）
- Columbia University（哥伦比亚大学）
- Université Paris-Saclay（巴黎萨克雷大学）
- University of Amsterdam（阿姆斯特丹大学）
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