论文标题
通过主要成分分析对各向异性量子厅状态中几何形状的研究
A Study of Geometry in Anisotropic Quantum Hall States by Principal Component Analysis
论文作者
论文摘要
在存在质量各向异性，各向异性相互作用或平面磁场的情况下，量子大厅液滴可以表现出形状变形和内部几何自由度。我们通过主成分分析表征了量子霍尔状态的几何形状，这是一种统计技术，强调数据集中的变化。我们首先在磁盘几何形状中具有偶极 - 偶极相互作用的整数量子大厅液滴中测试该方法。在随后在圆环几何形状中具有各向异性库仑相互作用的分数量子霍尔系统的应用中，我们证明了主要成分分析可以量化自由度的度量，并预测$ν= 1/3 $状态的崩溃。我们还计算填充分数时对相互作用各向异性的度量响应$ν= 1/5 $和$ 2/5 $，并表明在同一Ja那教序列中响应大致相同，但是在大偏序中，对于不同序列而言可能会有所不同。
In the presence of mass anisotropy, anisotropic interaction, or in-plane magnetic field, quantum Hall droplets can exhibit shape deformation and internal geometrical degree of freedom. We characterize the geometry of quantum Hall states by principal component analysis, which is a statistical technique that emphasizes variation in a dataset. We first test the method in an integer quantum Hall droplet with dipole-dipole interaction in disk geometry. In the subsequent application to fractional quantum Hall systems with anisotropic Coulomb interaction in torus geometry, we demonstrate that the principal component analysis can quantify the metric degree of freedom and predict the collapse of a $ν= 1/3$ state. We also calculate the metric response to interaction anisotropy at filling fractions $ν= 1/5$ and $2/5$ and show that the response is roughly the same within the same Jain sequence, but can differ at large anisotropy for different sequences.
