https://doi.org/10.1007/s100510050464
Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level*
1
Institut für Theoretische Physik, Universität Leipzig,
Augustusplatz 10, 04109 Leipzig, Germany
2
Physikalisch-Technische Bundesanstalt,
Bundesallee 100, 38116 Braunschweig, Germany
Corresponding author: a weller@itp.uni-leipzig.de
Received:
19
February
1998
Revised:
25
March
1998
Accepted:
17
April
1998
Published online: 15 October 1998
We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current- and charge-density exactly, without any expansion with respect to frequency or wave vector, we find that the integral for the ground-state energy converges rapidly (algebraically) at large wave vectors k, but exhibits a logarithmic divergence at small k. This divergence originates in the k-2 singularity of the Chern-Simons interaction and it is already present in lowest-order perturbation theory. A similar divergence appears in the chemical potential. Beyond the RPA, we identify diagrams for the grand-canonical potential (ladder-type, maximally crossed, or a combination of both) which diverge with powers of the logarithm. We expand our result for the RPA ground-state energy in the strength of the Coulomb interaction. The linear term is finite and its value compares well with numerical simulations of interacting electrons in the lowest Landau level.
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, 1998
