J. Phys. I France
Volume 4, Numéro 5, May 1994
Page(s) 737 - 756
DOI: 10.1051/jp1:1994173
J. Phys. I France 4 (1994) 737-756

Breakdown of the Fermi Liquid picture in one dimensional fermion systems: connection with the energy level statistics

R. Mélin, B. Douçot and P. Butaud

CRTBT-CNRS, BP 166X, 38042 Grenoble Cedex, France

(Received 22 October 1993, accepted 17 January 1994)

Using the adiabatic switching of interactions, we establish a condition for the existence of electronic quasiparticles in a Luttinger liquid. It involves a characteristic interaction strength proportional to the inverse square root of the system length. An investigation of the exact energy level separation probability distribution shows that this interaction scale also corresponds to a cross-over from the non interacting behaviour to a rather typical case for integrable systems, namely an exponential distribution. The level spacing statistics of a spin 1/2, one branch Luttinger model are also analyzed, as well as the level statistics of a two coupled chain model.

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