论文标题
FQH系统中拓扑数量的蒙特卡洛模拟
The Monte Carlo simulation of the topological quantities in FQH systems
论文作者
论文摘要
一般而言，对于分数量子厅（FQH）态，每个Landau轨道的电子职业数量可以从数值方法中获得，例如精确的对角线化，密度矩阵恢复归一化组或代数递归方案（杰克多项式）。在这项工作中，我们使用Metroplis Monte Carlo方法来计算圆柱几何形状中几个FQH状态的职业数量。使用40多个颗粒的收敛占用数来验证手性波音边缘理论，并通过动量极化或偶极矩确定拓扑量。不同拓扑领域的指导中心自旋，中央电荷和拓扑自旋与理论值和其他数值研究一致。特别是，我们获得了摩尔阅读和331个州的$ E/4 $ Quasihole的拓扑旋转。最后，我们计算了电子边缘绿色的功能和分析位置的依赖性。
Generally speaking, for a fractional quantum Hall (FQH) state, the electronic occupation number for each Landau orbit could be obtained from numerical methods such as exact diagonalization, density matrix renormalization group or algebraic recursive schemes (Jack polynomial). In this work, we apply a Metroplis Monte Carlo method to calculate the occupation numbers of several FQH states in cylinder geometry. The convergent occupation numbers for more than 40 particles are used to verify the chiral bosonic edge theory and determine the topological quantities via momentum polarization or dipole moment. The guiding center spin, central charge and topological spin of different topological sectors are consistent with theoretical values and other numerical studies. Especially, we obtain the topological spin of $e/4$ quasihole in Moore-Read and 331 states. At last, we calculate the electron edge Green's functions and analysis position dependence of the non-Fermi liquid behavior.
