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Fermi surface renormalization and quantum confinement in the two-coupled chains model

We address the problem of the Fermi surface renormalization and the quantum confinement regime (QCR) in the two coupled chains model(TCCM) of spinless fermions. We perform a self-consistent calculation of the renormalization group(RG) flows of the renormalized TCCM couplings and quasiparticle weight. On top of that we take explicitly into account the renormalization of the Fermi surface. The flow of the difference of the renormalized Fermi wave vectors associated with the bonding and antibonding bands has a dramatic effect on the single particle spectrum. Although the quasiparticle amplitude is nullified already at intermediate coupling the QCR is only observed at strong coupling. The state associated with this regime has a charge gap and it is not a Luttinger liquid. In contrast, the Fermi liquid regime is stabilized by the umklapp "$g_2$--like" interactions at very weak coupling regime.