Europhys. Lett.
Volume 74, Number 5, June 2006
Page(s) 785 - 791
Section General
Published online 05 May 2006
Europhys. Lett., 74 (5), pp. 785-791 (2006)
DOI: 10.1209/epl/i2006-10034-8

1D composite fermions: Bogoliubov-like mode in the Tonks-Girardeau gas

I. 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: $\omega(q)=q \sqrt{\bar\rho U(q)/m}$, where $\bar\rho$ 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.

© EDP Sciences 2006