标题： Hubbard相互作用对量子度量的影响 显示英文标题

标题： Effects of the Hubbard interaction on the quantum metric

摘要： 量子几何为各种形式的量子物质中的量子态结构和拓扑提供了重要的信息。 其中包含的信息对超导权重、德鲁德权重和光学响应等可观测量有深远的影响。 受近期在平坦能带相互作用系统中进展的启发，我们研究了相互作用效应对量子度规的作用。 通过使用费米子克鲁茨阶梯作为代表性系统，我们表明排斥型哈伯德相互作用会单调地抑制量子度规。 尽管在存在相互作用的情况下，可以通过精确对角化准确获得本征态及其量化量子度规的重叠，但这种方法仅适用于小尺寸系统。 另一种理论提议，广义量子度规和修饰量子度规，建议使用重整化的格林函数来定义相互作用量子度规。 通过将这些解析方法与精确对角化的结果进行比较，我们表明修饰量子度规能够更好地拟合精确对角化结果。 我们的结论适用于平坦能带和色散系统。 显示英文摘要

摘要： Quantum geometry provides important information about the structure and topology of quantum states in various forms of quantum matter. The information contained therein has profound effects on observable quantities such as superconducting weight, Drude weight, and optical responses. Motivated by the recent advances in flat-band interacting systems, we investigate the role of interaction effects on the quantum metric. By using the fermionic Creutz ladder as a representative system, we show that the repulsive Hubbard interaction monotonically suppresses the quantum metric. While the eigenstates and their overlap quantifying the quantum metric can be obtained exactly in the presence of interactions through exact diagonalization, this method is limited to small system sizes. Alternatively, two theoretical proposals, the generalized quantum metric and the dressed quantum metric, suggest using renormalized Green's functions to define the interacting quantum metric. By comparing these analytical approaches with results from exact diagonalization, we show that the dressed quantum metric provides a better fit to the exact diagonalization results. Our conclusion holds for both flat-band and dispersive systems.