  The ground-state properties of two-component bosonic mixtures in a
one-dimensional optical lattice are studied both from few- and many-body
perspectives. We rely directly on a microscopic Hamiltonian with attractive
inter-component and repulsive intra-component interactions to demonstrate the
formation of a quantum liquid. We reveal that its formation and stability can
be interpreted in terms of finite-range interactions between dimers. We derive
an effective model of composite bosons (dimers) which correctly captures both
the few- and many-body properties and validate it against exact results
obtained by DMRG method for the full Hamiltonian. The threshold for the
formation of the liquid coincides with the appearance of a bound state in the
dimer-dimer problem and possesses a universality in terms of the two-body
parameters of the dimer-dimer interaction, namely scattering length and
effective range. For sufficiently strong effective dimer-dimer repulsion we
observe fermionization of the dimers which form an effective Tonks-Girardeau
state. Finally, we identify conditions for the formation of a solitonic
solution.
