标题： 通过密度泛函理论和蒙特卡罗方法在圆盘上模拟复合费米子激子 显示英文标题

标题： Simulating Composite Fermion Excitons by Density Functional Theory and Monte Carlo on a Disk

摘要： Kohn-Sham密度泛函方法用于分数量子霍尔（FQH）效应最近被开发出来，通过将强相互作用的电子映射到一个辅助系统，该系统由弱相互作用的复合费米子（CFs）组成，这些复合费米子经历一个与密度相关的有效磁场。这种方法已被成功应用于探索边缘重构、准粒子激发的分数电荷和分数编织统计。在本工作中，我们研究了圆盘几何结构中体内的复合费米子激子。通过改变准粒子-准空穴对的分离并计算它们的能量，我们将磁旋子模式的色散与其它数值方法的结果进行比较，例如精确对角化（ED）和蒙特卡罗（MC）模拟。此外，通过评估谱函数，我们识别出手性“引力子”激发：对于类似粒子的Laughlin态为自旋$-2$模式，对于类似空穴的Laughlin态为自旋$2$模式。该方法可以扩展到构建其他圆盘几何结构中的分数量子霍尔态的中性集体激发。 显示英文摘要

摘要： The Kohn-Sham density functional method for the fractional quantum Hall (FQH) effect has recently been developed by mapping the strongly interacting electrons into an auxiliary system of weakly interacting composite fermions (CFs) that experience a density-dependent effective magnetic field. This approach has been successfully applied to explore the edge rescontruction, fractional charge and fractional braiding statistics of quasiparticle excitations. In this work, we investigate composite fermion excitons in the bulk of the disk geometry. By varying the separation of the quasiparticle-quasihole pairs and calculating their energy, we compare the dispersion of the magnetoroton mode with results from other numerical methods, such as exact diagonalization (ED) and Monte Carlo (MC) simulation. Furthermore, through an evaluation of the spectral function, we identify chiral ``graviton'' excitations: a spin $-2$ mode for the particle-like Laughlin state and a spin $2$ mode for the hole-like Laughlin state. This method can be extended to construct neutral collective excitations for other fractional quantum Hall states in disk geometry.