  We investigate the Hubbard Hamiltonian on ladders where the number of sites
per rung alternates between two and three. These geometries are bipartite, with
a non-equal number of sites on the two sublattices. Thus they share a key
feature of the Hubbard model in a class of lattices which Lieb has shown
analytically to exhibit long-range ferrimagnetic order, while being amenable to
powerful numeric approaches developed for quasi-one-dimensional geometries. The
Density Matrix Renormalization Group (DMRG) method is used to obtain the ground
state properties, e.g. excitation gaps, charge and spin densities as well as
their correlation functions at half-filling. We show the existence of
long-range ferrimagnetic order in the one-dimensional ladder geometries. Our
work provides detailed quantitative results which complement the general
theorem of Lieb for generalized bipartite lattices. It also addresses the issue
of how the alternation between quasi-long range order and spin liquid behavior
for uniform ladders with odd and even numbers of legs might be affected by a
regular alternation pattern.
