https://doi.org/10.1007/s100510170328
Ground state energy calculations of the v=1/2 and the v=5/2 FQHE system
Institut für Theoretische Physik, Universität Leipzig,
Augustusplatz 10, 04109 Leipzig, Germany
Corresponding author: a juergen.dietel@itp.uni-leipzig.de
Received:
13
June
2000
Published online: 15 January 2001
We reconsider energy calculations of the spin polarized
Chern-Simons theory.
We show that one has to be careful in the definition of the Chern-Simons
path integral in order to avoid an IR divergent magnetic ground state energy
in RPA as in [J. Dietel et al, Eur. Phys. J. B 5, 439 (1998)]. We correct the path integral and
get a well behaved magnetic
energy by considering the energy of the maximal divergent graphs
as well as the Hartree-Fock graphs. Furthermore, we consider the 
and the 
system
with spin degrees of freedom. In doing this we formulate a Chern-Simons theory
of the 
system by transforming the interaction operator
to the next lower Landau level. We calculate the Coulomb energy
of the spin polarized as well as
the spin unpolarized and the system as a function of the
interaction strength in RPA.
These energies are in good agreement with numerical simulations of interacting electrons
in the first as well as in the second Landau level. Furthermore, we calculate
the compressibility, the effective mass and the excitations of the
spin polarized 
systems where 
is an
even number.
PACS: 71.10.Pm – Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) / 73.40.Hm – Quantum Hall effect (integer and fractional) / 71.27.+a – Strongly correlated electron systems; heavy fermions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
