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A single-particle path integral for composite fermions and the renormalization of the effective mass

Kasper Astrup Eriksen·Per Hedegaard·Henrik Bruus
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Abstract

To study composite fermions around an even denominator fraction, we adapt the phase space single-particle path integral technique for interacting electrons in zero magnetic field developed recently by D.S. Golubev and A.D. Zaikin, Phys. Rev. B {\bf 59}, 9195 (1999). This path integral description gives an intuitive picture of composite fermion propagation very similar to the Caldeira-Leggett treatment of a particle interacting with an external environment. We use the new description to explain the origin of the famous cancellation between the self-energy and the vertex corrections in semi-classical transport measurements. The effective range of the cancellation is given by the size of the propagating particle, which for the Coulomb interaction scales with the temperature T as T^{-1/4} |log T|^{-1} in the semi-classical limit. Using this scheme we find that the effective mass in the semi-classical limit for composite fermions in GaAs is approximately 6 times the bare mass.

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Kasper Astrup Eriksen, Per Hedegaard, Henrik Bruus. 2001-01-09. A single-particle path integral for composite fermions and the renormalization of the effective mass. https://doi.org/10.1103/physrevb.64.195327

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