论文标题
分数量子厅状态的光谱响应函数的自相似性
Self-similarity of spectral response functions for fractional quantum Hall states
论文作者
论文摘要
光谱响应函数是量子多体状态分析的中心量，因为它们描述了多体系统对外部扰动的响应，因此直接对应于实验中可观察的物体。在本文中，我们使用持续分数方法来评估Fermionic $ν= 1/3 $分数量子霍尔状态的动量平均动力密度结构因子。我们建立了相对于相互作用范围的筛选库仑结构因子的缩放行为，并暴露了频域中结构因子的固有自相似性。这些结果突出了分数量子霍尔状态的光谱响应函数的统计特性，并展示了如何在数值模型中有效地近似它们。
Spectral response functions are central quantities in the analysis of quantum many-body states, since they describe the response of many-body systems to external perturbations and hence directly correspond to observables in experiments. In this paper, we evaluate a momentum-averaged dynamical density structure factor for the fermionic $ν=1/3$ fractional quantum Hall state on a torus, using the continued fraction method to compute the dynamical correlation function. We establish the scaling behavior of the screened Coulomb structure factor with respect to interaction range, and expose an inherent self-similarity of structure factors in the frequency domain. These results highlight the statistical properties of spectral response functions for fractional quantum Hall states and show how they can be efficiently approximated in numerical models.
