Method of computation of energies in the fractional quantum Hall effect regime

Abstract

In a previous work, we reported exact results of energies of the ground state in the fractional quantum Hall effect (FQHE) regime for systems with up to $N_{\text{e}}=6$ electrons at the filling factor $\nu =1/3$ by using the method of complex polar coordinates. In this work, we display interesting computational details of the previous calculation and extend the calculation to $N_{\text{e}}=7$ electrons at $\nu =1/3$. Moreover, similar exact results are derived at the filling $\nu =1/5$ for systems with up to $N_{\text{e}}=6$ electrons. The results that we obtained by analytical calculation are in good agreement with their analogues ones derived by the method of Monte Carlo in a precedent work.

9 pages, 1 figure

References in corpus (2)

• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Monte Carlo simulation method for Laughlin-like states in a disk geometry

Cited by in corpus (2)

• Analytic results of the excited electronic states at $\upsilon =1/3$ and the Laughlin-Jain microscopic wave function approaches
• New exact analytical results for two quasiparticle excitation in the fractional quantum Hall effect