Does Luttinger liquid behaviour survive in an atomic wire on a surface?

We form a highly simplified model of an atomic wire on a surface by the coupling of two one-dimensional chains, one with electron-electron interactions to represent the wire and one with no electron-electron interactions to represent the surface. We use exact-diagonalization techniques to calculate the eigenstates and response functions of our model, in order to determine both the nature of the coupling and to what extent the coupling affects the Luttinger liquid properties that we would expect in a purely one-dimensional system. We find that while there are indeed Luttinger liquid indicators present, some residual Fermi liquid characteristics remain.