Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level |
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Authors: | J Dietel T Koschny W Apel W Weller |
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Institution: | Institut für Theoretische Physik, Universit?t Leipzig, Augustusplatz 10, 04109 Leipzig, Germany, DE Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany, DE
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Abstract: | 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.
Received: 19 February 1998 / Revised: 25 March 1998 / Accepted: 17 April 1998 |
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Keywords: | 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 |
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