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

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

1993-11-19

arxiv.org/abs/cond-mat/9311047v2

Physics

Condensed Matter

22 pages, Latex

Scientific paper

10.1051/jp1:1994173

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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