标题： 量子几何在非厄米拓扑相变附近的尺度行为 显示英文标题

标题： Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions

摘要： 量子态的几何性可以作为临界性的指标，但在非厄米拓扑条件下仍较少被探索。在这项工作中，我们揭示了在Kitaev链的非厄米长程扩展中接近不同拓扑相变时，基态流形上量子几何的多样化缩放行为。几何相位导数及其缩放行为表明，具有不同长程耦合的系统可以属于不同的普适类。在某些临界点附近，我们进一步发现与基态扩展贝里联络相关的Wannier态关联函数表现出空间上的异常行为。最后，我们在例外点附近的相变处分析了量子几何张量的缩放行为，阐明了新型普适类的出现。 显示英文摘要

摘要： The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold close to different topological phase transitions in a non-Hermitian long-range extension of the Kitaev chain. The derivative of the geometric phase, as well as its scaling behavior, shows that systems with different long-range couplings can belong to distinct universality classes. Near certain criticalities, we further find that the Wannier state correlation function associated with extended Berry connection of the ground state exhibits spatially anomalous behaviors. Finally, we analyze the scaling of the quantum geometric tensor near phase transitions across exceptional points, shedding light on the emergence of novel universality classes.