The ground-state phase diagram of Heisenberg spin-1/2 system on a two-leg
ladder with rung alternation is studied by combining analytical approaches with
numerical simulations. For the case of ferromagnetic leg exchanges a unique
ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic
leg exchanges several different ground states are stabilized depending on the
ratio between exchanges along legs and rungs. For the more general case of a
honeycomb-ladder model for the case of ferromagnetic leg exchanges besides
usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic
Luttinger liquid phase with both linear and quadratic low energy dispersions
and ground state magnetization continuously changing with system parameters.
For the case of antiferromagnetic exchanges along legs, different dimerized
states including states with additional topological order are suggested to be
realized
