Diverging Heisenberg spin ladders: ground state and low energy excitations.

We consider a two-leg ladder system with interactions varying from constant rung coupling to systematic diminishing of rung interactions leading to diverging chains. We compare and contrast their ground state and excitation characteristics using density matrix renormalization group methods. We find that the finite spin gap in a constant coupling ladder develops into a gapless excitation with slight diminishing of the distance dependent coupling. Varying the spatial range of the rung coupling, we derive the effective length scale of triplet excitations in these ladder classes of systems.