1D composite fermions: Bogoliubov-like mode in the Tonks-Girardeau gasI. V. Ovchinnikov and D. Neuhauser
Department of Chemistry and Biochemistry, University of California at Los Angeles Los Angeles, CA, 90095-1569, USA
received 24 February 2006; accepted 4 April 2006
published online 5 May 2006
We reformulate 1D boson-fermion duality in path-integral terms. The result is a 1D counterpart of the boson-fermion duality in the 2D Chern-Simons gauge theory. The theory is consistent and enables, using standard resummation techniques, to obtain the long-wavelength asymptotics of the collective mode in 1D boson systems at the Tonks-Girardeau regime. The collective mode has the dispersion of Bogoliubov phonons: , where is the bosons density and U(q) is a Fourier component of the two-body potential.
05.30.Jp - Boson systems.
71.10.Pm - Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.).
71.45.Gm - Exchange, correlation, dielectric and magnetic response functions, plasmons.
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