Single-particle states in weakly coupled linear chains

The validity of the quasiparticle picture for electrons in weakly coupled linear chains is investigated using for a single chain the Tomonaga-Luttinger model of interacting one-dimensional electrons. For interchain coupling without jumps between the chains it is proved exactly that no stable quasiparticles exist. The excitation spectrum is exhausted by density oscillations and the single-particle occupation number shows a power-law behavior. For finite-interchain hopping, lowest-order-perturbation theory yields a quasiparticle peak in the spectral density. Its weight is $z={[1-2\mathrm{}\alpha \ln (\frac{W_{\perp }}{W_{\parallel }}\left)\right]}^{-1\mathrm{}}$, where $\alpha$ is the interaction parameter and $W_{\parallel }$ and $W_{\perp }$ are the widths of the conduction band in momentum direction parallel and perpendicular to the chains. The relevance of our results for real quasi-one-dimensional conductors will be discussed.