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Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level

J. Dietel·Th. Koschny·W. Apel·W. Weller
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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 1/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.

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J. Dietel, Th. Koschny, W. Apel, W. Weller. 1998-02-26. Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level. https://doi.org/10.1007/s100510050464

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