发表机构
University of Bologna; Julius-Maximilians-Universität Würzburg; Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（博洛尼亚大学; 维尔茨堡大学; 上海数学与交叉学科研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究揭示量子几何可将QBT处非微扰的指数小能隙放大为代数增强的响应，并通过解析与kagome模型验证，确立量子几何作为非微扰尺度的渐近放大器。
AI 中文摘要
二维二次能带交叉点（QBT）处的弱相互作用可以产生指数小的对称性破缺能隙，$m\sim e^{-A/V_1}$，该能隙无法被任何有限阶微扰论捕捉。我们证明，有能隙QBT的奇异量子几何将该超越所有阶的尺度转化为代数增强的响应。量子度量发展出一个动量空间热点，其布里渊区积分对数发散，因此当能隙由相互作用动态产生时，该积分代数增长。通过逆频率Souza--Wilkens--Martin光学求和规则，相同的放大出现在负一阶纵向光学矩中，尽管普通光学电导率仍为$O(e^2/\hbar)$且其吸收阈值指数小。我们针对大质量QBT解析地建立了这些结果，并在一个已知在其QBT处由环电流序自发产生量子反常霍尔质量的可相互作用kagome晶格模型中微观验证了它们。我们的结果将量子几何识别为非微扰相互作用尺度的渐近放大器。
英文摘要
Weak interactions at a two-dimensional quadratic band touching (QBT) can generate an exponentially small symmetry-breaking gap, $m\sim e^{-A/V_1}$, that cannot be captured by every finite order of perturbation theory. We show that the singular quantum geometry of the gapped QBT converts this beyond-all-orders scale into an algebraically enhanced response. The quantum metric develops a momentum-space hot spot whose Brillouin-zone integral diverges logarithmically, and therefore grows algebraically when the gap is dynamically generated by interactions. Through the inverse-frequency Souza--Wilkens--Martin optical sum rule, the same amplification appears in the negative-first longitudinal optical moment, even though the ordinary optical conductivity remains $O(e^2/\hbar)$ and its absorption threshold is exponentially small. We establish these results analytically for a massive QBT and verify them microscopically in an interacting kagome lattice model known to develop a spontaneous quantum anomalous Hall mass at its QBT from loop currents order. Our results identify quantum geometry as an asymptotic amplifier of nonperturbative interaction scales.
CommentsWe welcome any suggestion and comment about content and missing important references. Main text consists of 5 pages + references. Supplemental Material consists of 68 pages
