The Monte Carlo simulation of the topological quantities in FQH systems

TL;DR

This paper uses Monte Carlo simulations to compute topological properties of fractional quantum Hall states, verifying theoretical predictions and exploring edge behaviors in large systems.

Contribution

It introduces a Monte Carlo approach to calculate occupation numbers and topological quantities in FQH systems, extending analysis to larger particle numbers.

Findings

Occupation numbers converge for over 40 particles

Topological quantities match theoretical and previous numerical results

Topological spin of e/4 quasihole obtained for Moore-Read and 331 states

Abstract

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.