AI 中文总结
该研究揭示平带中RKKY相互作用由布洛赫态量子几何介导，量子度量决定磁关联长度、自旋刚度及有限体系临界温度，规避Mermin-Wagner定理约束。
AI 中文摘要
平带导带使群速度猝灭，对基于色散的Ruderman-Kittel-Kasuya-Yosida（RKKY）相互作用的传统图像提出挑战，传统图像中局域磁矩通过导带电子介导的有效交换耦合。本文表明，平带极限下的RKKY相互作用不会因群速度消失而消失，反而由布洛赫态的量子几何介导。从微观RKKY推导出发，我们证明布里渊区平均的量子度量控制静态磁化率的长波结构，从而确定磁关联长度和自旋刚度。因此，即使单粒子色散不存在，瓦尼尔函数的有限空间扩展也提供了有效的长程耦合通道。此外，我们确立了有限和低维样品中有序温度由量子度量控制的一般原理，有效规避了Mermin-Wagner定理的热力学极限约束。具体而言，我们的理论研究表明，在有限尺寸系统中，增大量子度量会增强磁刚性，进而导致临界温度相应升高。
英文摘要
Flat conduction bands quench the group velocity and thus challenge conventional, dispersion-driven pictures of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, where localized moments are coupled via an effective exchange mediated by conduction electrons. Here we show that RKKY interactions in the flat-band limit are not extinguished by the vanishing group velocity but are instead mediated by the quantum geometry of Bloch states. Starting from a microscopic RKKY derivation, we demonstrate that the Brillouin-zone-averaged quantum metric controls the long-wavelength structure of the static susceptibility, thereby determining the magnetic correlation length and the spin stiffness. As a result, the finite spatial spread of Wannier functions provides an effective long-range coupling channel even when single-particle dispersion is absent. Furthermore, we establish the general principle that the ordering temperature is governed by the quantum metric in finite and low-dimensional samples, effectively circumventing the thermodynamic-limit constraint of the Mermin-Wagner theorem. Specifically, our theoretical investigation reveals that increasing the quantum metric enhances magnetic rigidity and leads to a corresponding rise in the critical temperature within finite-sized systems.
Comments5 pages, 4 Figures
