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

Abstract

We study the effect of a transverse hopping ${\mathit{t}}_{\mathrm{\perp }}$ 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, ${\mathit{t}}_{\mathrm{\perp }}$ 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 ${\mathit{t}}_{\mathrm{\perp }}$. 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 ${\mathit{t}}_{\mathrm{\perp }}$, 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 ${\mathit{t}}_{\mathrm{\perp }}$ does modify the shape of the Fermi surface. The asymptotic expression of the single-particle Green function is also obtained.