一维手性量子系统拓扑相变中的对数输运
Logarithmic transport at topological phase transitions of one-dimensional chiral quantum systems
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- Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）
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中文总结 AI 辅助
本文研究一维手性量子系统在无序驱动拓扑相变中的输运，发现位置算符矩呈对数增长，机制源于最小本征值本征函数近似为经典随机游走的指数，形成两个亚指数局域中心。
中文摘要 AI 辅助
随机跳跃哈密顿量是一维手性哈密顿量中无序驱动的拓扑相变的一个玩具模型。它具有消失的Lyapunov指数，并且在零能量处态密度出现Dyson峰。这项工作展示了量子动力学如何导致位置算符各阶矩的对数增长，类似于经典Sinai扩散中的行为。这一现象背后的机制是，最小本征值对应的本征函数可以很好地由经典随机游走的指数来近似，从而产生两个本质上独立的亚指数局域中心。
英文摘要
The random hopping Hamiltonian is a toy model for a disorder-driven topological phase transitions in one-dimensional chiral Hamiltonians. It has a vanishing Lyapunov exponent and a Dyson peak in the density of states at zero energy. This work shows how the quantum dynamics leads to a logarithmic growth of the moments of the position operator, similar as in classical Sinai diffusion. The mechanism at the origin of this phenomenon is that the eigenfunction of the smallest eigenvalue is well-approximated by the exponential of a classical random walk, leading to two essentially independent subexponential localization centers.
