Monte Carlo simulation of the topological quantities in fractional quantum Hall systems

Generally speaking, for a fractional quantum Hall (FQH) state, the electronic occupation number for each Landau orbit could be obtained by numerical methods such as exact diagonalization, density matrix renormalization group, matrix product state, or algebraic recursive schemes (Jack polynomial). In this paper, we apply a Metropolis 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 topological quantities from momentum polarization or dipole moments. The guiding center spin, central charge, and topological spin of different topological sectors are consistent with theoretical values and other numerical studies. In particular, we obtain the topological spin of a e /4 quasihole in Moore-Read and 331 states. Lastly, we calculate the electron edge Green's functions and analyze the position dependence of the non-Fermi liquid behavior.