Universal scaling behavior of coupled chains of interacting fermions

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 $t_{\perp }$ is shown to become unstable in the thermodynamic limit. The single-chain anomalous exponent $\alpha$ [characterizing the low-energy density of state $N\left(\omega \right)\sim {\omega }^{\alpha }]$ is shown to be the key parameter that governs the finite-size scaling behavior. In the regime $\alpha <{\alpha }_{2p}$ $({\alpha }_{2p}\simeq 0.41)$ 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 $t_{\perp }^{\alpha /\left(1\mathrm{}-\alpha \right)},$ in agreement with a random-phase-approximation–like treatment of the interchain coupling. For $\alpha >{\alpha }_{2p},$ the scaling law is proved to change its functional form, thus signaling the onset of coherent transverse two-particle hopping.