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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. The field of strongly correlated electron systems has recently stimulated interesting discussions which are sometimes challenging some more traditional ideas on the many body problem. For instance, Anderson has proposed that the low energy properties of a two dimensional Hubbard model are not properly described by a Fermi liquid theory [1]. In a recent paper [2], he emphasizes that this question requires a non perturbative treatment, and a careful consideration of boundary conditions. As a consequence of the difficulty of the problem, a lot o

Year: 1995

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