Role of transverse hopping in a two-coupled-chains model

We study the effect of a transverse hopping tperpendicular in two chains of both spinless and spinning repulsively interacting fermions, by means of renormalization group and bosonization techniques. We show that, independent of the presence of spin, tperpendicular strongly modifies the asymptotic long-wavelength behavior of the two chains, opening gaps in the excitation spectra. The origin of the instability of the gapless Luttinger-liquid behavior is identified in the flavor (==chain index) anisotropy induced by tperpendicular. In the case of spinning fermions, it leads to dominant pair fluctuations, in spite of the repulsive interaction. The role of spin is further analyzed in a model of two coupled chains showing, in the absence of tperpendicular, spin-charge separation without anomalous exponents. We solve this model exactly by the bosonization technique, and we find that the interesting analytical properties induced by spin-charge separation persist in the presence of transverse hopping, although tperpendicular does modify the shape of the Fermi surface. The asymptotic expression of the single-particle Green function is also obtained