Condensed Matter Physics, 2016, vol. 19, No. 3, 33702
DOI:10.5488/CMP.19.33702
arXiv:1609.04713
Title:
Method of computation of energies in the fractional quantum Hall effect regime
Author(s):

M.A. Ammar
(Environment Department, University of Medea, 26000 Media, Algeria)
,


Z. Bentalha
(Theoretical Physics Laboratory, University of Tlemcen, B.P. 230, 13000 Tlemcen, Algeria)
,


S. Bekhechi
(Theoretical Physics Laboratory, University of Tlemcen, B.P. 230, 13000 Tlemcen, Algeria)

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_{e}=6 electrons at the filling factor ν=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_{e}=7 electrons at ν=1/3. Moreover, similar exact results are derived at the filling ν=1/5 for systems with up to N_{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.
Key words:
quantum Hall effect, 2D electron gas, manybody wave function, strongly correlated system
PACS:
73.43.f, 73.43.Cd, 71.10.Ca, 02.70.Wz
