https://doi.org/10.1140/epjb/e20020094
The asymptotic behaviour of the exact and approximative ν=1/2 Chern-Simons Green's functions
Institut für Theoretische Physik, Universität Leipzig,
Augustusplatz 10, 04109 Leipzig, Germany
Corresponding author: a dietel@itp.uni-leipzig.de
Received:
5
July
2001
Revised:
30
November
2001
Published online: 15 April 2002
We consider the asymptotic behaviour of the Chern-Simons Green's function
of the
system for an infinite area in position-time
representation. We calculate explicitly the
asymptotic form of the Green's function of the interaction free Chern-Simons
system for small times. The calculated Green's function
vanishes exponentially with the
logarithm of the area. Furthermore, we discuss the form of the divergence
for all 
and also for the Coulomb interacting Chern-Simons system.
We compare the asymptotics of the exact Chern-Simons
Green's function with the asymptotics of the Green's function in the
Hartree-Fock
as well as the random-phase approximation (RPA).
The asymptotics of the Hartree-Fock Green's function correspondence well
with the exact Green's function. In the case of the
RPA Green's function we do not get the correct asymptotics.
At last, we calculate the
self consistent Hartree-Fock Green's function.
PACS: 71.10.Pm – Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) / 73.43.-f – Quantum Hall effects / 71.27.+a – Strongly correlated electron systems; heavy fermions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002
