Universal scaling behavior of coupled chains of interacting fermions

Abstract

The single-particle hopping between two chains is investigated by exact-diagonalization techniques supplemented by finite-size scaling analysis. In the case of two coupled strongly correlated chains of spinless fermions, the Taylor expansion of the expectation value of the single-particle interchain hopping operator of an electron at momentum ${k}_{F}$ in powers of the interchain hopping ${t}_{\ensuremath{\perp}}$ is shown to become unstable in the thermodynamic limit. The single-chain anomalous exponent $\ensuremath{\alpha}$ [characterizing the low-energy density of state $N(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{\alpha}}]$ is shown to be the key parameter that governs the finite-size scaling behavior. In the regime $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{2p}$ $({\ensuremath{\alpha}}_{2p}\ensuremath{\simeq}0.41)$ where transverse two-particle hopping is less relevant than single-particle hopping, the finite-size effects can be described in terms of a universal scaling function. From this analysis it is found that the single-particle transverse hopping behaves as ${t}_{\ensuremath{\perp}}^{\ensuremath{\alpha}/(1\ensuremath{-}\ensuremath{\alpha})},$ in agreement with a random-phase-approximation--like treatment of the interchain coupling. For $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{2p},$ the scaling law is proved to change its functional form, thus signaling the onset of coherent transverse two-particle hopping.